Gravitational Waves from Binary Black Holes · Gravitational Waves from Binary Black Holes Bala...

Gravitational Waves from Binary Black Holes

Bala Iyer

Raman Research Institute,Bangalore, India

Chandrasekhar Centenary Conference,IIA, 7th December 2010

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Bala Iyer (RRI) GW from BBH 7 December 2010 1 / 53

Einstein’s equations and Gravitational Waves (GW)

If a Theory of Gravitation is consistent with Principle of SpecialRelativity the Effect of Gravity cannot be transmitted Faster thanLight.

If Grav Field of an object changes, the changes propagate thro’ spaceand take a Finite time to reach other objects. These propagatingoscillations are called Gravitational Radiation or Gravitational Waves

Einstein’s Theory of Gravitation (General Relativity) is consistent withSR and predicts GW

In GR, GW travel with the speed of light, are transverse and have twostates of polarisation just like EMW

Conservation of energy rules out monopole gravitational radn.Conservn of Lin Mom and Ang Mom forbid gravitational dipole radn

GW intrinsically non-linear since wave energy density itself ‘gravitates’

GW propagate essentially unperturbed thro space (UncorruptedViews) as they interact weakly with matter (Tough to Detect)















































Einstein’s equations and Gravitational Waves

1916: In the paper exploring physical implications of GTR, Einsteinproposed existence of GW as one of its important consequences

1918: Einstein calculated flux of energy far from sourceQuadrupole Formula ..Radiation Reaction ..Radiation Damping.Distinguished between Energy carrying physical waves vsnon-energy carrying wave-like coordinate (gauge) artefacts ..

1922: Eddington: Corrected factor of 2 in AE’s work, pointedinapplicability of AE’s derivation for self gravitating systems.Described the situation regarding gauge effects he said:GW propagate at speed of thought!

Appears Einstein wished to forget he had predicted GW.Reasonable judgement about slim chance that GW might be detected.




















Improved theoretical understanding of GW

Landau Lifshiftz (1941) and Fock (1955) extended Quadrupoleformula to weakly self-grav systems.. Constitute two differentapproaches (DIRE and MPM) to GW generation today..

Conservative PN dynamics is an expansion in v2/c2. With this choiceof expn parameter, nPN means corrections of order (v2/c2)n relativeto leading order..2.5PN EOM means EOM corrrect up to v5/c5

Complication: For self-gravitating systems orders in velocity arerelated to orders in non-linearity..Virial theorem → Φ = GM/R sameorder as v2 ..Reaction terms of order (v/c)5 from linear theory will beaccompanied by terms (v/c)3 Φ/c2, (v/c)1 (Φ/c2)2..Higher order PN calculation requires dealing dealing withhigher order non-linearities.1950 + Goldberg, Havas, Pirani, Bondi, Metzner, Sachs ..Mathematically precise discussion of Asymptotics in GR.Rigorous work that GW transfer energy!More physically, Feynman, Bondi showed..GW could in principle heat a suitably contrived mechanical system!



Landau Lifshiftz (1941) and Fock (1955) extended Quadrupoleformula to weakly self-grav systems.. Constitute two differentapproaches (DIRE and MPM) to GW generation today..Conservative PN dynamics is an expansion in v2/c2. With this choiceof expn parameter, nPN means corrections of order (v2/c2)n relativeto leading order..2.5PN EOM means EOM corrrect up to v5/c5





Complication: For self-gravitating systems orders in velocity arerelated to orders in non-linearity..Virial theorem → Φ = GM/R sameorder as v2 ..Reaction terms of order (v/c)5 from linear theory will beaccompanied by terms (v/c)3 Φ/c2, (v/c)1 (Φ/c2)2..Higher order PN calculation requires dealing dealing withhigher order non-linearities.

1950 + Goldberg, Havas, Pirani, Bondi, Metzner, Sachs ..Mathematically precise discussion of Asymptotics in GR.Rigorous work that GW transfer energy!More physically, Feynman, Bondi showed..GW could in principle heat a suitably contrived mechanical system!




Complication: For self-gravitating systems orders in velocity arerelated to orders in non-linearity..Virial theorem → Φ = GM/R sameorder as v2 ..Reaction terms of order (v/c)5 from linear theory will beaccompanied by terms (v/c)3 Φ/c2, (v/c)1 (Φ/c2)2..Higher order PN calculation requires dealing dealing withhigher order non-linearities.1950 + Goldberg, Havas, Pirani, Bondi, Metzner, Sachs ..Mathematically precise discussion of Asymptotics in GR.Rigorous work that GW transfer energy!

More physically, Feynman, Bondi showed..GW could in principle heat a suitably contrived mechanical system!






Chandrasekhar’s Contributions

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Influence of GR on pulsation and stability of starsChandra, Friedman, Schutz..

PN approximations to GR and its Ap applicationsNutku, Esposito

Back reaction of GW on their sourcesEinstein, EIH, Trautman, Fock, Burke-Thorne...

First direct calculation a la Lorentz of Radiation Reaction force inagreement with quadrupole radiation lossesPNA has become standard working tool of physics and Ap. Used instudies of stars, star clusters, gravitational wave generation, motion ofplanets and moon, development of PPN formalism to compare GRwith other theories of gravity and experimentIf Chandra had left us no other relativistic legacy

beyond the PN and PPN formalisms, he would stilldeserve a place among the great contributers to oursubject - Kip Thorne



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-








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First direct calculation a la Lorentz of Radiation Reaction force inagreement with quadrupole radiation losses

PNA has become standard working tool of physics and Ap. Used instudies of stars, star clusters, gravitational wave generation, motion ofplanets and moon, development of PPN formalism to compare GRwith other theories of gravity and experimentIf Chandra had left us no other relativistic legacy




-




First direct calculation a la Lorentz of Radiation Reaction force inagreement with quadrupole radiation lossesPNA has become standard working tool of physics and Ap. Used instudies of stars, star clusters, gravitational wave generation, motion ofplanets and moon, development of PPN formalism to compare GRwith other theories of gravity and experiment

If Chandra had left us no other relativistic legacybeyond the PN and PPN formalisms, he would stilldeserve a place among the great contributers to oursubject - Kip Thorne



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Chandrasekhar (Oct 19 1910 - 1995 ) and GW - (Schutz JAA 17, 183 1996)

1960’s: Chandrasekhar - Radiation Reaction problem.. How doesemission of GW affect the emitting system when its self-gravitating?

Chandra was first to show conceptually that radiation reactionproblem could be solved for continuous systems..

Damping, null and even anti-damping results existed.. Confusedsituation led some to doubt reality of gravitational radiation andpossibility of associating some kind of conserved energy with GW..Unsatisfactory from both physical and Astrophysics pts of view.

Chandra saw the need for a careful step by step approach startingfrom Newtonian limit and proceeding PN order by order. No one hadattempted PN approximation for continuous bodies in an exhaustiveway..

Realised that previous works used simplifications that could have ledto fallacies .. Decided to avoid any tricks..Do a complete and honestcalculation. Studied previous works until he knew what to emulateand what to discard






























Chandrasekhar and GW - (Schutz JAA 17, 183 1996)

Technical issues concerned use of point particles and the relatedinfinite self-field energy problems in a non-linear theory, imposition ofno-incoming boundary condition in a PN scheme, dealing withconservative (even in v/c) and dissipative (odd in v/c) effectsseparately, validity of the use of matched asymptotic expansions toisolate terms in EOM coupling to radiation far away..

Assembled together the essential ingredients: Landau-Lifshiftzpseudo-tensor to include the non-linearities of the Grav field,Retarded potentials and near-zone expansion to implement outgoingBC following Trautman.Gave astrophysicists confidence that GR was physically reasonableand well behaved. Energy and AM radiated as GW was correctlybalanced by the loss of mechanical energy and AMImportant applications immediately followed:(i) GW induced non-axisymmetric instability of rotating stars(ii) Faulkner: Cataclysmic binary systems: Competition of GW RRand mass transfer



Technical issues concerned use of point particles and the relatedinfinite self-field energy problems in a non-linear theory, imposition ofno-incoming boundary condition in a PN scheme, dealing withconservative (even in v/c) and dissipative (odd in v/c) effectsseparately, validity of the use of matched asymptotic expansions toisolate terms in EOM coupling to radiation far away..Assembled together the essential ingredients: Landau-Lifshiftzpseudo-tensor to include the non-linearities of the Grav field,Retarded potentials and near-zone expansion to implement outgoingBC following Trautman.

Gave astrophysicists confidence that GR was physically reasonableand well behaved. Energy and AM radiated as GW was correctlybalanced by the loss of mechanical energy and AMImportant applications immediately followed:(i) GW induced non-axisymmetric instability of rotating stars(ii) Faulkner: Cataclysmic binary systems: Competition of GW RRand mass transfer



Technical issues concerned use of point particles and the relatedinfinite self-field energy problems in a non-linear theory, imposition ofno-incoming boundary condition in a PN scheme, dealing withconservative (even in v/c) and dissipative (odd in v/c) effectsseparately, validity of the use of matched asymptotic expansions toisolate terms in EOM coupling to radiation far away..Assembled together the essential ingredients: Landau-Lifshiftzpseudo-tensor to include the non-linearities of the Grav field,Retarded potentials and near-zone expansion to implement outgoingBC following Trautman.Gave astrophysicists confidence that GR was physically reasonableand well behaved. Energy and AM radiated as GW was correctlybalanced by the loss of mechanical energy and AM

Important applications immediately followed:(i) GW induced non-axisymmetric instability of rotating stars(ii) Faulkner: Cataclysmic binary systems: Competition of GW RRand mass transfer



Technical issues concerned use of point particles and the relatedinfinite self-field energy problems in a non-linear theory, imposition ofno-incoming boundary condition in a PN scheme, dealing withconservative (even in v/c) and dissipative (odd in v/c) effectsseparately, validity of the use of matched asymptotic expansions toisolate terms in EOM coupling to radiation far away..Assembled together the essential ingredients: Landau-Lifshiftzpseudo-tensor to include the non-linearities of the Grav field,Retarded potentials and near-zone expansion to implement outgoingBC following Trautman.Gave astrophysicists confidence that GR was physically reasonableand well behaved. Energy and AM radiated as GW was correctlybalanced by the loss of mechanical energy and AMImportant applications immediately followed:(i) GW induced non-axisymmetric instability of rotating stars(ii) Faulkner: Cataclysmic binary systems: Competition of GW RRand mass transfer



However there were problems: (i) (in the gauge he chose to work in)some terms at 2PN were divergent..Expressions only formal??

(ii) Appearance of terms diverging at infinity for continuous sourcesand reconcilation only by accepting for metric a solution only in thedistributional senseThe divergences cast doubt on the validity of Chandra’s treatment formore mathematically demanding relativists and proved to be a barrierfor extension of the treatment to higher PN orders..Chandra (and Thorne) did not find the infinities worrying becausethey felt they had a physicists intuition for the correctness of themethod used and results obtained. By brute force, insight andattention to detail, Chandra first achieved what many relativists hadtried for decades.Chandra unhappy about the criticism reg divergent terms since itprevented him from being given adequate credit for significance of hisPN work. Only body of work not immortalized by a book unlike allhis other research endeavours!!



However there were problems: (i) (in the gauge he chose to work in)some terms at 2PN were divergent..Expressions only formal??(ii) Appearance of terms diverging at infinity for continuous sourcesand reconcilation only by accepting for metric a solution only in thedistributional sense

The divergences cast doubt on the validity of Chandra’s treatment formore mathematically demanding relativists and proved to be a barrierfor extension of the treatment to higher PN orders..Chandra (and Thorne) did not find the infinities worrying becausethey felt they had a physicists intuition for the correctness of themethod used and results obtained. By brute force, insight andattention to detail, Chandra first achieved what many relativists hadtried for decades.Chandra unhappy about the criticism reg divergent terms since itprevented him from being given adequate credit for significance of hisPN work. Only body of work not immortalized by a book unlike allhis other research endeavours!!



However there were problems: (i) (in the gauge he chose to work in)some terms at 2PN were divergent..Expressions only formal??(ii) Appearance of terms diverging at infinity for continuous sourcesand reconcilation only by accepting for metric a solution only in thedistributional senseThe divergences cast doubt on the validity of Chandra’s treatment formore mathematically demanding relativists and proved to be a barrierfor extension of the treatment to higher PN orders..

Chandra (and Thorne) did not find the infinities worrying becausethey felt they had a physicists intuition for the correctness of themethod used and results obtained. By brute force, insight andattention to detail, Chandra first achieved what many relativists hadtried for decades.Chandra unhappy about the criticism reg divergent terms since itprevented him from being given adequate credit for significance of hisPN work. Only body of work not immortalized by a book unlike allhis other research endeavours!!



However there were problems: (i) (in the gauge he chose to work in)some terms at 2PN were divergent..Expressions only formal??(ii) Appearance of terms diverging at infinity for continuous sourcesand reconcilation only by accepting for metric a solution only in thedistributional senseThe divergences cast doubt on the validity of Chandra’s treatment formore mathematically demanding relativists and proved to be a barrierfor extension of the treatment to higher PN orders..Chandra (and Thorne) did not find the infinities worrying becausethey felt they had a physicists intuition for the correctness of themethod used and results obtained. By brute force, insight andattention to detail, Chandra first achieved what many relativists hadtried for decades.

Chandra unhappy about the criticism reg divergent terms since itprevented him from being given adequate credit for significance of hisPN work. Only body of work not immortalized by a book unlike allhis other research endeavours!!



However there were problems: (i) (in the gauge he chose to work in)some terms at 2PN were divergent..Expressions only formal??(ii) Appearance of terms diverging at infinity for continuous sourcesand reconcilation only by accepting for metric a solution only in thedistributional senseThe divergences cast doubt on the validity of Chandra’s treatment formore mathematically demanding relativists and proved to be a barrierfor extension of the treatment to higher PN orders..Chandra (and Thorne) did not find the infinities worrying becausethey felt they had a physicists intuition for the correctness of themethod used and results obtained. By brute force, insight andattention to detail, Chandra first achieved what many relativists hadtried for decades.Chandra unhappy about the criticism reg divergent terms since itprevented him from being given adequate credit for significance of hisPN work. Only body of work not immortalized by a book unlike allhis other research endeavours!!


A century of waiting...

Almost 100 years since GW were theoretically predicted but still noexperimental confirmation a la Hertz

Reason is connected to two fundamental differences between EM andGravitation:The weakness of the gravitational interaction relative to EM (10−39)andThe spin two nature of gravitation compared to the spin one natureof EM that forbids dipole radiation in GR.

Implies low efficiency for conversion of mechanical energy togravitational radiation. And feeble effects of GW on any potentialdetector. A GW Hertz experiment is ruled out and it is only signalsproduced by astrophysical systems where there are potentially hugemasses accelerating very strongly that are likely sources.












Gravitational Waves exist

High quality data ∼ Proof that GW exist

In 1974 Hulse and Taylor,

Discovered the Binary Pulsar 1913+16 -

The system has now been monitored for ∼ 30 years




















Indeed ..Gravitational Waves exist ..

If General relativity is right (and Newtonian Gravity is incorrect) thesystem must emit GW. Orbit shrinks by 3 mm/orbit..

Orbital period slowly decreasing at just the rate predicted by GR for emission of GW!!!

Hulse and Taylor received Nobel Prize for this (1993).


Quadrupole Formula controversy??

Prospects of testing PN theory against Hulse-Taylor system onceagain revived more critical questions (Kerlick, Ehlers, Havas..)regarding existing treatment of GW (Chandrasekhar, Thorne..)

(i) Does it apply to orbital motion of the two NS even though it doesnot apply to their internal structure with strong gravitational fields?

(ii) Even for weak fields is it a valid approximation of GR due to thedivergent terms in the PN equations?

(i) Needs methods to treat weak orbital fields without assumption oninternal fields. Can show orbits and interactions of stars independentof compactness modulo tidal distortions - 1980’s,early 90’s Bel et al,

Damour-Deruelle, Damour, Futamase and Schutz, Walker-Will, Grischuk-Kopeijkin

(ii) If radiation is present, inconvenient to iterate usingNewtonian-like Poisson equations.. Retardation effects cannot beneglected..Successful formalisms are all formulated in terms ofretarded integrals rather than Poisson-like Green functions..(Damour, Blanchet, Will and Walker, Thorne, Haridass and Soni...)


































Genesis of Mark II Approximation Methods

The high quality binary pulsar data forced a revisit to approximationmethods in GR to remedy the mathematical shortcomings in theexisting approaches

Insights of a newer generation more comfortable with techniques infield theory to deal with divergences helped

Damour (thesis on regularisation in classical field theories) criticallylooked at the problem and realised the need to carefully deal with UVdivergences arising from the use of Delta functions to model pointparticles in a non-linear thory.. Proposed iteration algorithmsincluding Riesz regularisation to deal with such divergences

Iterated Einstein’s Eqns to sufficient order of non-linearity to obtainEOM of compact binaries including v5/c5 terms (1983)(Einstein-Infeld-Hoffmann approach)

ai = aNewtoni + a1PN

i + a2PNi + a2.5PN

i

Laplace-Eddington effect (at 2.5PN)








i + a2PNi + a2.5PN

i









i + a2PNi + a2.5PN

i









i + a2PNi + a2.5PN

i



Laser Interferometric Gravitational Wave Detectors?

Binary Pulsars establish Reality of Grav Radn. Validity of GR inStrong Fields. Excellent Evidence but Evidence is Indirect

Can detectors be built to attempt a Direct detection of these GW??GW are transverse and tidally distort a system in directionsperpendicular to propagation direction (Pirani, Weber).Effect measured by the Dimensionless strain h = 2(∆L)/L it producesFor a typical NS binary in Virgo cluster (18 Mpc; 5.6× 1020 km)h ∼ 4G

c4DKnonsph ∼ 2 GM

Rc2GMDc2 ∼ 1.5× 10−21.

The miniscule strain and associated tiny displacement must bemeasured to detect the GW. Weber’s Bar detectors (Narrow band);Today’s Laser Interferometeric Detectors ( Broad Band)As a GW passes, the arm lengths of km scale ITF change (10−18m)tidally causing the interference pattern to change at the photodiodeDirect detection of GW -First mandate of Laser Interferometric GW detectorsPromised and Real Excitement - New Observational Window andTool for Astrophysics; Experimental Probe for Basic Physics



Binary Pulsars establish Reality of Grav Radn. Validity of GR inStrong Fields. Excellent Evidence but Evidence is IndirectCan detectors be built to attempt a Direct detection of these GW??

GW are transverse and tidally distort a system in directionsperpendicular to propagation direction (Pirani, Weber).Effect measured by the Dimensionless strain h = 2(∆L)/L it producesFor a typical NS binary in Virgo cluster (18 Mpc; 5.6× 1020 km)h ∼ 4G

c4DKnonsph ∼ 2 GM

Rc2GMDc2 ∼ 1.5× 10−21.




Binary Pulsars establish Reality of Grav Radn. Validity of GR inStrong Fields. Excellent Evidence but Evidence is IndirectCan detectors be built to attempt a Direct detection of these GW??GW are transverse and tidally distort a system in directionsperpendicular to propagation direction (Pirani, Weber).Effect measured by the Dimensionless strain h = 2(∆L)/L it produces

For a typical NS binary in Virgo cluster (18 Mpc; 5.6× 1020 km)h ∼ 4G

c4DKnonsph ∼ 2 GM

Rc2GMDc2 ∼ 1.5× 10−21.




Binary Pulsars establish Reality of Grav Radn. Validity of GR inStrong Fields. Excellent Evidence but Evidence is IndirectCan detectors be built to attempt a Direct detection of these GW??GW are transverse and tidally distort a system in directionsperpendicular to propagation direction (Pirani, Weber).Effect measured by the Dimensionless strain h = 2(∆L)/L it producesFor a typical NS binary in Virgo cluster (18 Mpc; 5.6× 1020 km)h ∼ 4G

c4DKnonsph ∼ 2 GM

Rc2GMDc2 ∼ 1.5× 10−21.





c4DKnonsph ∼ 2 GM

Rc2GMDc2 ∼ 1.5× 10−21.

The miniscule strain and associated tiny displacement must bemeasured to detect the GW. Weber’s Bar detectors (Narrow band);Today’s Laser Interferometeric Detectors ( Broad Band)

As a GW passes, the arm lengths of km scale ITF change (10−18m)tidally causing the interference pattern to change at the photodiodeDirect detection of GW -First mandate of Laser Interferometric GW detectorsPromised and Real Excitement - New Observational Window andTool for Astrophysics; Experimental Probe for Basic Physics




c4DKnonsph ∼ 2 GM

Rc2GMDc2 ∼ 1.5× 10−21.

The miniscule strain and associated tiny displacement must bemeasured to detect the GW. Weber’s Bar detectors (Narrow band);Today’s Laser Interferometeric Detectors ( Broad Band)As a GW passes, the arm lengths of km scale ITF change (10−18m)tidally causing the interference pattern to change at the photodiode

Direct detection of GW -First mandate of Laser Interferometric GW detectorsPromised and Real Excitement - New Observational Window andTool for Astrophysics; Experimental Probe for Basic Physics




c4DKnonsph ∼ 2 GM

Rc2GMDc2 ∼ 1.5× 10−21.

The miniscule strain and associated tiny displacement must bemeasured to detect the GW. Weber’s Bar detectors (Narrow band);Today’s Laser Interferometeric Detectors ( Broad Band)As a GW passes, the arm lengths of km scale ITF change (10−18m)tidally causing the interference pattern to change at the photodiodeDirect detection of GW -First mandate of Laser Interferometric GW detectors

Promised and Real Excitement - New Observational Window andTool for Astrophysics; Experimental Probe for Basic Physics




c4DKnonsph ∼ 2 GM

Rc2GMDc2 ∼ 1.5× 10−21.



LIGO and Virgo TODAY

Field reached a Milestone with decades-old plans to build and operate largeinterferometric GW detectors now realized at several locations worldwide

S5: Nov 2005 -Sep 2007; Some Joint runs with Virgo; LIGO Science Collbn, Virgo collabn

Unprecedented sensitivity allows one to place Upper Limits on GW from a variety of Ap

sources..Bala Iyer (RRI) GW from BBH 7 December 2010 15 / 53

Future Improvements in Detector sensitivity

GW detectors are sensitive to Amplitude of the radiation which fallsof as inverse of the Source Distance. Factor N increase in sensitivityleads to N3 increase in Probed Volume and hence Event Rates.

From inception LIGO and Virgo envisaged as an ongoingObservatory.. Infrastructure to go to higher sensitivityEnhanced Detectors (2009 -11); 2× sensitivity; 8× event rate35W Laser power; more efficient readout for GW channel

LIGO and Virgo will be upgraded to Advanced Detectors (2015 - )12× increase in sensitivity; Over 1000× increase in rateSignal recycling, 200W laser, Test mass 40 kg (↓ radn pr noise), Larger beams, better

dielelectric mirror coatings, four cascaded stages of passive isolation, fused silica fibers

(low mech loss, reduce susp noise 100×), two-stage active isolation, go down to 10 Hz

Einstein Telescope (2027 - ): 3G Detector100× increase in sensitivity; Over 106× increase in rateET: Conceptual design study( EC; 3 years; 3M Euros; Sathyaprakash)Laser Interferometer Space Antenna (LISA); 5 million km baseline;Low freq GW from SMBH; (NASA-ESA, 2025)



GW detectors are sensitive to Amplitude of the radiation which fallsof as inverse of the Source Distance. Factor N increase in sensitivityleads to N3 increase in Probed Volume and hence Event Rates.From inception LIGO and Virgo envisaged as an ongoingObservatory.. Infrastructure to go to higher sensitivity

Enhanced Detectors (2009 -11); 2× sensitivity; 8× event rate35W Laser power; more efficient readout for GW channel







GW detectors are sensitive to Amplitude of the radiation which fallsof as inverse of the Source Distance. Factor N increase in sensitivityleads to N3 increase in Probed Volume and hence Event Rates.From inception LIGO and Virgo envisaged as an ongoingObservatory.. Infrastructure to go to higher sensitivityEnhanced Detectors (2009 -11); 2× sensitivity; 8× event rate35W Laser power; more efficient readout for GW channel




















Expected Annual Coalescence Rates

In a 95% confidence interval, rates uncertain by 3 orders of magnitudeNS-NS (0.4− 400); NS-BH (0.2.− 300) ; BH-BH (2.− 4000) yr−1

Based on Extrapolations from obsvd Bin Psrs,Stellar birth rateestimates, Population Synthesis modelsRates quoted below are mean of the distribution.

Detector NS-NS NS-BH BH-BH

Initial LIGO0.02 0.0006 0.0009

(2002-06)

Enhanced LIGO×2 sensitivity 0.1 0.04 0.07

(2009-10)

Advanced LIGO×12 sensitivity 40 10 20

(2014+)


Black Hole Binaries and the next decade

Evidence of BH in universe on a range of mass scales: Stellar massBH (3− 30)M�; IMBH (102 − 104)M�; MBH (104 − 109)M�

BH mergers monumental Astrophysical events releasing tremendousamounts of energy in form of GW .. Releases more power thancombined light from all stars in visible universe..Key sources for bothground based and space based GW detectorsBH and GW, two exotic and amazing predictions of GR, cometogether in Binary BH - Expected to be strongest emitters of GWSuccessful direct detection and opening of GW astronomy would relyheavily on the global network of GW observatories set up at optimallocations.New observatories are required for improved duty cycle, improved skycoverage, polarization coverage, enhanced signal to noise ratio andmost importantly improved angular resolution.Recent report of the Gravitational Wave International Committee(GWIC) recognizes the need for a detector in Asia-Pacific region –Japan, Australia, and in the future possibly India and China



Evidence of BH in universe on a range of mass scales: Stellar massBH (3− 30)M�; IMBH (102 − 104)M�; MBH (104 − 109)M�BH mergers monumental Astrophysical events releasing tremendousamounts of energy in form of GW .. Releases more power thancombined light from all stars in visible universe..Key sources for bothground based and space based GW detectors

BH and GW, two exotic and amazing predictions of GR, cometogether in Binary BH - Expected to be strongest emitters of GWSuccessful direct detection and opening of GW astronomy would relyheavily on the global network of GW observatories set up at optimallocations.New observatories are required for improved duty cycle, improved skycoverage, polarization coverage, enhanced signal to noise ratio andmost importantly improved angular resolution.Recent report of the Gravitational Wave International Committee(GWIC) recognizes the need for a detector in Asia-Pacific region –Japan, Australia, and in the future possibly India and China



Evidence of BH in universe on a range of mass scales: Stellar massBH (3− 30)M�; IMBH (102 − 104)M�; MBH (104 − 109)M�BH mergers monumental Astrophysical events releasing tremendousamounts of energy in form of GW .. Releases more power thancombined light from all stars in visible universe..Key sources for bothground based and space based GW detectorsBH and GW, two exotic and amazing predictions of GR, cometogether in Binary BH - Expected to be strongest emitters of GW

Successful direct detection and opening of GW astronomy would relyheavily on the global network of GW observatories set up at optimallocations.New observatories are required for improved duty cycle, improved skycoverage, polarization coverage, enhanced signal to noise ratio andmost importantly improved angular resolution.Recent report of the Gravitational Wave International Committee(GWIC) recognizes the need for a detector in Asia-Pacific region –Japan, Australia, and in the future possibly India and China



Evidence of BH in universe on a range of mass scales: Stellar massBH (3− 30)M�; IMBH (102 − 104)M�; MBH (104 − 109)M�BH mergers monumental Astrophysical events releasing tremendousamounts of energy in form of GW .. Releases more power thancombined light from all stars in visible universe..Key sources for bothground based and space based GW detectorsBH and GW, two exotic and amazing predictions of GR, cometogether in Binary BH - Expected to be strongest emitters of GWSuccessful direct detection and opening of GW astronomy would relyheavily on the global network of GW observatories set up at optimallocations.

New observatories are required for improved duty cycle, improved skycoverage, polarization coverage, enhanced signal to noise ratio andmost importantly improved angular resolution.Recent report of the Gravitational Wave International Committee(GWIC) recognizes the need for a detector in Asia-Pacific region –Japan, Australia, and in the future possibly India and China



Evidence of BH in universe on a range of mass scales: Stellar massBH (3− 30)M�; IMBH (102 − 104)M�; MBH (104 − 109)M�BH mergers monumental Astrophysical events releasing tremendousamounts of energy in form of GW .. Releases more power thancombined light from all stars in visible universe..Key sources for bothground based and space based GW detectorsBH and GW, two exotic and amazing predictions of GR, cometogether in Binary BH - Expected to be strongest emitters of GWSuccessful direct detection and opening of GW astronomy would relyheavily on the global network of GW observatories set up at optimallocations.New observatories are required for improved duty cycle, improved skycoverage, polarization coverage, enhanced signal to noise ratio andmost importantly improved angular resolution.

Recent report of the Gravitational Wave International Committee(GWIC) recognizes the need for a detector in Asia-Pacific region –Japan, Australia, and in the future possibly India and China



Evidence of BH in universe on a range of mass scales: Stellar massBH (3− 30)M�; IMBH (102 − 104)M�; MBH (104 − 109)M�BH mergers monumental Astrophysical events releasing tremendousamounts of energy in form of GW .. Releases more power thancombined light from all stars in visible universe..Key sources for bothground based and space based GW detectorsBH and GW, two exotic and amazing predictions of GR, cometogether in Binary BH - Expected to be strongest emitters of GWSuccessful direct detection and opening of GW astronomy would relyheavily on the global network of GW observatories set up at optimallocations.New observatories are required for improved duty cycle, improved skycoverage, polarization coverage, enhanced signal to noise ratio andmost importantly improved angular resolution.Recent report of the Gravitational Wave International Committee(GWIC) recognizes the need for a detector in Asia-Pacific region –Japan, Australia, and in the future possibly India and China


Towards GW Astronomy - LIGO - Australia

LIGO Hanford Livingston + VirgoWen and Chen

+ LIGO AustraliaWen and Chen

US LIGO has agreed to transfer to Australia an advanced GW detectorprovided Australia funds construction of National facility to house it andcommits to running costs for 10 years. NSF has approved LIGO-Australiaprovided ACIGA makes a commitment before end of 2011IndIGO (Indian Initiative in GW Observations) Consortium plans to seekfunds to collaborate with ACIGA and participate in LIGO-Australia.










US LIGO has agreed to transfer to Australia an advanced GW detectorprovided Australia funds construction of National facility to house it andcommits to running costs for 10 years. NSF has approved LIGO-Australiaprovided ACIGA makes a commitment before end of 2011

IndIGO (Indian Initiative in GW Observations) Consortium plans to seekfunds to collaborate with ACIGA and participate in LIGO-Australia.







Future Proposed Global GW Network

LCGT: Large Scale Cryogenic Gravitational Wave Telescope

Courtesy: Stan WhitcombBala Iyer (RRI) GW from BBH 7 December 2010 20 / 53

LISA & LIGO Cover 10 Orders of Magnitude

EMW Studied over 20 Orders of Magnitude(ULF Radio (103 Hz; 106 m)- HE γ rays (1022 Hz; 10−13 m)(VLF GW (10−7 Hz - 10−9 Hz) ; ELF GW (10−15 Hz - 10−18 Hz)


The Last Three Minutes..Can Chirping Binaries be detected?

Can we detect the GW from 1913+16 today???No! Since Porb ∼ 8 hrs, fGW ∼ 10−4 Hz. Interferometers on Earthcannot be sensitive at this frequency due to seismic noise.

However, due to gravitational radiation reaction the binary spirals inwith ever increasing velocity and frequency and increasing amplitudedue to the stronger gravitational fieldThus, in 300 million years fGW ∼ 10 Hz. 15 minutes later fGW ∼ 1000Hz. 16,000 cycles in the last three minutes before coalescence. Allthis brings the system in the sensitivity bandwidths of Earth bounddetectors. Eccentricity would reduce from e = .617 to e → 0.In 2003 a new binary (Double) pulsar J0737-3039 with orbital periodof 2.5 hrs (e = .0877) was discovered which will coalesce in 86 Myrs.Infall due to Grav radn Damping 7 mm/day!Even more unique Laboratory for relativistic gravitational physics inthe strong field regime



Can we detect the GW from 1913+16 today???No! Since Porb ∼ 8 hrs, fGW ∼ 10−4 Hz. Interferometers on Earthcannot be sensitive at this frequency due to seismic noise.However, due to gravitational radiation reaction the binary spirals inwith ever increasing velocity and frequency and increasing amplitudedue to the stronger gravitational field

Thus, in 300 million years fGW ∼ 10 Hz. 15 minutes later fGW ∼ 1000Hz. 16,000 cycles in the last three minutes before coalescence. Allthis brings the system in the sensitivity bandwidths of Earth bounddetectors. Eccentricity would reduce from e = .617 to e → 0.In 2003 a new binary (Double) pulsar J0737-3039 with orbital periodof 2.5 hrs (e = .0877) was discovered which will coalesce in 86 Myrs.Infall due to Grav radn Damping 7 mm/day!Even more unique Laboratory for relativistic gravitational physics inthe strong field regime



Can we detect the GW from 1913+16 today???No! Since Porb ∼ 8 hrs, fGW ∼ 10−4 Hz. Interferometers on Earthcannot be sensitive at this frequency due to seismic noise.However, due to gravitational radiation reaction the binary spirals inwith ever increasing velocity and frequency and increasing amplitudedue to the stronger gravitational fieldThus, in 300 million years fGW ∼ 10 Hz. 15 minutes later fGW ∼ 1000Hz. 16,000 cycles in the last three minutes before coalescence. Allthis brings the system in the sensitivity bandwidths of Earth bounddetectors. Eccentricity would reduce from e = .617 to e → 0.

In 2003 a new binary (Double) pulsar J0737-3039 with orbital periodof 2.5 hrs (e = .0877) was discovered which will coalesce in 86 Myrs.Infall due to Grav radn Damping 7 mm/day!Even more unique Laboratory for relativistic gravitational physics inthe strong field regime



Can we detect the GW from 1913+16 today???No! Since Porb ∼ 8 hrs, fGW ∼ 10−4 Hz. Interferometers on Earthcannot be sensitive at this frequency due to seismic noise.However, due to gravitational radiation reaction the binary spirals inwith ever increasing velocity and frequency and increasing amplitudedue to the stronger gravitational fieldThus, in 300 million years fGW ∼ 10 Hz. 15 minutes later fGW ∼ 1000Hz. 16,000 cycles in the last three minutes before coalescence. Allthis brings the system in the sensitivity bandwidths of Earth bounddetectors. Eccentricity would reduce from e = .617 to e → 0.In 2003 a new binary (Double) pulsar J0737-3039 with orbital periodof 2.5 hrs (e = .0877) was discovered which will coalesce in 86 Myrs.Infall due to Grav radn Damping 7 mm/day!Even more unique Laboratory for relativistic gravitational physics inthe strong field regime


Prototype Sources - Inspiralling Compact Binaries

Late Inspiral and Merger Epochs of compact binaries of neutron starsor black holes provide us possible strong sources of GW for LIGO andVirgo in the ‘high’ frequency range 10 Hz - 10 kHz

We have guaranteed sources for the GW detectors if there are enoughof them.

The waveform is a chirpAmplitude and Frequency increasing with Time

GW are WEAK SIGNALS buried in NOISE of detector

Require Matched Filtering (MF) both for their Detection orExtraction and Parameter Estimation or Characterisation

Success of MF requires Accurate model of signal using Gen Rel;

Favours sources like ICB (NS-NS, BH-BH, NS-BH) over unmodelledsources like supernovae or GRB - Led to Progress in 2-bodyproblem in GR

































































Chirp Signal, Matched Filtering

Courtesy Anand Sengupta (IUCAA)


GW from ICB - Cutler et al 1993

When LIGO was funded in early nineties, and efforts to constructaccurate ICB waveforms started, it was soon realised that far higherorder PN accurate waveforms would be needed to approximate GW inthe final stages of inspiral and merger than in Binary Psr work

Numerical Relativity was far from mature and a Grand ChallengeProgram was started towards this goalPhysical insights were essential to simplify the goals and achieve therequired waveforms..They include(i) Garden variety ICB would have radiated away their eccentricityand be moving in quasi-circular orbits during the late inspiral(ii) Since matched filtering is sensitive to the phase it is moreimportant to first control higher order phasing than higher orderamplitudes - Newtonian Amplitude + Best available phasing:Restricted waveform(iii) The inspiral can be treated in the adiabatic approximation as asequences of circular orbits..This allows one to treat separately theradiation reaction effects and the conservative effects



When LIGO was funded in early nineties, and efforts to constructaccurate ICB waveforms started, it was soon realised that far higherorder PN accurate waveforms would be needed to approximate GW inthe final stages of inspiral and merger than in Binary Psr workNumerical Relativity was far from mature and a Grand ChallengeProgram was started towards this goal

Physical insights were essential to simplify the goals and achieve therequired waveforms..They include(i) Garden variety ICB would have radiated away their eccentricityand be moving in quasi-circular orbits during the late inspiral(ii) Since matched filtering is sensitive to the phase it is moreimportant to first control higher order phasing than higher orderamplitudes - Newtonian Amplitude + Best available phasing:Restricted waveform(iii) The inspiral can be treated in the adiabatic approximation as asequences of circular orbits..This allows one to treat separately theradiation reaction effects and the conservative effects



When LIGO was funded in early nineties, and efforts to constructaccurate ICB waveforms started, it was soon realised that far higherorder PN accurate waveforms would be needed to approximate GW inthe final stages of inspiral and merger than in Binary Psr workNumerical Relativity was far from mature and a Grand ChallengeProgram was started towards this goalPhysical insights were essential to simplify the goals and achieve therequired waveforms..They include

(i) Garden variety ICB would have radiated away their eccentricityand be moving in quasi-circular orbits during the late inspiral(ii) Since matched filtering is sensitive to the phase it is moreimportant to first control higher order phasing than higher orderamplitudes - Newtonian Amplitude + Best available phasing:Restricted waveform(iii) The inspiral can be treated in the adiabatic approximation as asequences of circular orbits..This allows one to treat separately theradiation reaction effects and the conservative effects



When LIGO was funded in early nineties, and efforts to constructaccurate ICB waveforms started, it was soon realised that far higherorder PN accurate waveforms would be needed to approximate GW inthe final stages of inspiral and merger than in Binary Psr workNumerical Relativity was far from mature and a Grand ChallengeProgram was started towards this goalPhysical insights were essential to simplify the goals and achieve therequired waveforms..They include(i) Garden variety ICB would have radiated away their eccentricityand be moving in quasi-circular orbits during the late inspiral

(ii) Since matched filtering is sensitive to the phase it is moreimportant to first control higher order phasing than higher orderamplitudes - Newtonian Amplitude + Best available phasing:Restricted waveform(iii) The inspiral can be treated in the adiabatic approximation as asequences of circular orbits..This allows one to treat separately theradiation reaction effects and the conservative effects



When LIGO was funded in early nineties, and efforts to constructaccurate ICB waveforms started, it was soon realised that far higherorder PN accurate waveforms would be needed to approximate GW inthe final stages of inspiral and merger than in Binary Psr workNumerical Relativity was far from mature and a Grand ChallengeProgram was started towards this goalPhysical insights were essential to simplify the goals and achieve therequired waveforms..They include(i) Garden variety ICB would have radiated away their eccentricityand be moving in quasi-circular orbits during the late inspiral(ii) Since matched filtering is sensitive to the phase it is moreimportant to first control higher order phasing than higher orderamplitudes - Newtonian Amplitude + Best available phasing:Restricted waveform

(iii) The inspiral can be treated in the adiabatic approximation as asequences of circular orbits..This allows one to treat separately theradiation reaction effects and the conservative effects



When LIGO was funded in early nineties, and efforts to constructaccurate ICB waveforms started, it was soon realised that far higherorder PN accurate waveforms would be needed to approximate GW inthe final stages of inspiral and merger than in Binary Psr workNumerical Relativity was far from mature and a Grand ChallengeProgram was started towards this goalPhysical insights were essential to simplify the goals and achieve therequired waveforms..They include(i) Garden variety ICB would have radiated away their eccentricityand be moving in quasi-circular orbits during the late inspiral(ii) Since matched filtering is sensitive to the phase it is moreimportant to first control higher order phasing than higher orderamplitudes - Newtonian Amplitude + Best available phasing:Restricted waveform(iii) The inspiral can be treated in the adiabatic approximation as asequences of circular orbits..This allows one to treat separately theradiation reaction effects and the conservative effects


GW from ICB - Three Modules

(iii) One can go to higher PN orders in the inspiral without gettingtechnically bogged down in controlling the much more difficult higherorder conservative PN terms

(iv) For compact objects the effects of finite size and quadrupoledistortion induced by tidal interactions are of order 5PN. Hence,neutron stars and black holes can be modelled as point particlesrepresented by Dirac δ-functions.Thus modelling ICB waveforms involves three tasksMotion: Given a Binary system, iterate Einstein’s Eqns to discussconservative motion of the system. Compute CM Energy EGeneration: Given the motion of the binary system on a fixed orbit,iterate EE to compute multipoles of the Grav field and hence the FZflux of energy and AM carried by GW. Compute L and JRadiation Reaction: Given the Conserved energy and Radiated Flux ofEnergy and AM, ASSUME the Balance Eqns to Compute the effect ofRadiation on the Orbit. Compute F (t) and φ(t);(GW) Phasing of Binary ∼ (EMW) Timing of Pulsars



(iii) One can go to higher PN orders in the inspiral without gettingtechnically bogged down in controlling the much more difficult higherorder conservative PN terms(iv) For compact objects the effects of finite size and quadrupoledistortion induced by tidal interactions are of order 5PN. Hence,neutron stars and black holes can be modelled as point particlesrepresented by Dirac δ-functions.

Thus modelling ICB waveforms involves three tasksMotion: Given a Binary system, iterate Einstein’s Eqns to discussconservative motion of the system. Compute CM Energy EGeneration: Given the motion of the binary system on a fixed orbit,iterate EE to compute multipoles of the Grav field and hence the FZflux of energy and AM carried by GW. Compute L and JRadiation Reaction: Given the Conserved energy and Radiated Flux ofEnergy and AM, ASSUME the Balance Eqns to Compute the effect ofRadiation on the Orbit. Compute F (t) and φ(t);(GW) Phasing of Binary ∼ (EMW) Timing of Pulsars



(iii) One can go to higher PN orders in the inspiral without gettingtechnically bogged down in controlling the much more difficult higherorder conservative PN terms(iv) For compact objects the effects of finite size and quadrupoledistortion induced by tidal interactions are of order 5PN. Hence,neutron stars and black holes can be modelled as point particlesrepresented by Dirac δ-functions.Thus modelling ICB waveforms involves three tasks

Motion: Given a Binary system, iterate Einstein’s Eqns to discussconservative motion of the system. Compute CM Energy EGeneration: Given the motion of the binary system on a fixed orbit,iterate EE to compute multipoles of the Grav field and hence the FZflux of energy and AM carried by GW. Compute L and JRadiation Reaction: Given the Conserved energy and Radiated Flux ofEnergy and AM, ASSUME the Balance Eqns to Compute the effect ofRadiation on the Orbit. Compute F (t) and φ(t);(GW) Phasing of Binary ∼ (EMW) Timing of Pulsars



(iii) One can go to higher PN orders in the inspiral without gettingtechnically bogged down in controlling the much more difficult higherorder conservative PN terms(iv) For compact objects the effects of finite size and quadrupoledistortion induced by tidal interactions are of order 5PN. Hence,neutron stars and black holes can be modelled as point particlesrepresented by Dirac δ-functions.Thus modelling ICB waveforms involves three tasksMotion: Given a Binary system, iterate Einstein’s Eqns to discussconservative motion of the system. Compute CM Energy E

Generation: Given the motion of the binary system on a fixed orbit,iterate EE to compute multipoles of the Grav field and hence the FZflux of energy and AM carried by GW. Compute L and JRadiation Reaction: Given the Conserved energy and Radiated Flux ofEnergy and AM, ASSUME the Balance Eqns to Compute the effect ofRadiation on the Orbit. Compute F (t) and φ(t);(GW) Phasing of Binary ∼ (EMW) Timing of Pulsars



(iii) One can go to higher PN orders in the inspiral without gettingtechnically bogged down in controlling the much more difficult higherorder conservative PN terms(iv) For compact objects the effects of finite size and quadrupoledistortion induced by tidal interactions are of order 5PN. Hence,neutron stars and black holes can be modelled as point particlesrepresented by Dirac δ-functions.Thus modelling ICB waveforms involves three tasksMotion: Given a Binary system, iterate Einstein’s Eqns to discussconservative motion of the system. Compute CM Energy EGeneration: Given the motion of the binary system on a fixed orbit,iterate EE to compute multipoles of the Grav field and hence the FZflux of energy and AM carried by GW. Compute L and J

Radiation Reaction: Given the Conserved energy and Radiated Flux ofEnergy and AM, ASSUME the Balance Eqns to Compute the effect ofRadiation on the Orbit. Compute F (t) and φ(t);(GW) Phasing of Binary ∼ (EMW) Timing of Pulsars



(iii) One can go to higher PN orders in the inspiral without gettingtechnically bogged down in controlling the much more difficult higherorder conservative PN terms(iv) For compact objects the effects of finite size and quadrupoledistortion induced by tidal interactions are of order 5PN. Hence,neutron stars and black holes can be modelled as point particlesrepresented by Dirac δ-functions.Thus modelling ICB waveforms involves three tasksMotion: Given a Binary system, iterate Einstein’s Eqns to discussconservative motion of the system. Compute CM Energy EGeneration: Given the motion of the binary system on a fixed orbit,iterate EE to compute multipoles of the Grav field and hence the FZflux of energy and AM carried by GW. Compute L and JRadiation Reaction: Given the Conserved energy and Radiated Flux ofEnergy and AM, ASSUME the Balance Eqns to Compute the effect ofRadiation on the Orbit. Compute F (t) and φ(t);(GW) Phasing of Binary ∼ (EMW) Timing of Pulsars


Phasing Formula in the Adiabatic Approximation

In the adiabatic approximation and for restricted WF (GW phasetwice orbital phase) phasing specified by a pair of differential eqns

dφ

dt− v3

M= 0,

dv

dt+F(v)

ME ′(v)= 0,

F(v): GW Flux; E (v): Binding energy; Prime: deriv wrt v ;v = (πMF )1/3; x = v2,.

G = c = 1 M ∼ 5× 10−6(M/M�)s ∼ 1.5(M/M�)km


Major Technical Tools and Approximation Approaches

Multipole (M) expansions: Expansion in irreducible representations ofthe rotation group using STF tensors or tensor spherical harmonics

Post - Minkowskian (PM) approximation. Non-linearity expansion.Expn in G - Valid in the weak-field region including ∞.

Post - Newtonian (PN) approximation - Slow motion expn.Expn in v/c . Valid in the near zone.

Successful wave-generation formalisms are a subtle cocktail ofdifferent approaches. MPM + PN employed to deal with Arbitrarymass ratio inspiral in slow-motion weak field regime

Perturbation about BH ST - Test pcle Limit– Can deal with Extrememass ratio inspiral (EMRI); + Quasi-Normal Mode (QNM) ringing

Self-Force approach: µ/M corrections to above Perturbation results -extreme mass ratio inspiral even in strong field regime..

Beyond PNA; Pade Resummation; Effective one body approach:Inspiral, Late inspiral, merger, ringdown..

Numerical relativity for coalescence, merger and ringdown








































































Multipolar Post Minkowskian (MPM) formalism

There are two independent aspects addressing two different problems.

(i) The general method (MPM expansion) applicable to extended orfluid sources with compact support, based on the mixed PM andmultipole expansion matched to some PN (slowly moving, weaklygravitating, small-retardation) source. IR divergences arising from theretardation expansion dealt by analytic continuation

(ii) The particular application to describe inspiralling compact binaries(ICB) by use of point particle models. Self-field regularisation to dealwith UV divergences arising from use of Delta functions to modelpoint particles - Riesz, Hadamard partie finie, work well up to 2PN..Lead to ambiguities at 3PN both in EOM and Flux..Needed moresophisticated gauge invariant Dimensional regularisation for resolutionof the inconsistencies and completion of the problem.

hµν ≡ √−ggµν − ηµν , in the harmonic gauge ∂νhµν = 0,

EE reduces to 2fhµν = 16πTµν + Λµν [h, ∂h, ∂2h]

Λµν represents non-linear terms in EE.


























MPM Generation formalism

EE integrated using flat-space retarded integrals. To perform PNexpansion, one expands retarded integrals in powers of 1/c .Divergent integrals appear due to near-zone nature of PN expn.

The MPM generation formalism (Blanchet Damour BRI) followingFock essentially involves a Multipolar Post Minkowskian (MPM)expansion of the gravitational field in the region outside the sourceincluding infinity.

This is followed by a Post Newtonian (PN) expansion in the near zoneand their matching in an intermediate zone. (IR) Divergences handledby complex analytic continuation. This specifies the field exterior tothe source completely.

In the DIRE approach of Will Wiseman (LL EWT) retarded integralsevaluated beyond the near zone without expansion using nullcoordinates.





















In DimReg scheme, Look for soln of EE in D = d + 1 ST dimn withpt pcle matter source (Delta fn in d-dim).. d treated as cx numberand intermediate formulas in PN iteration of the eqns interpreted byanalytical continuation in it by d = 3 + ε. Neglect terms of order εand higher and retain finite part and eventual poles.

(F (x))1 =AC

ε→ 0[

limx→y1

F (x)]

MPM generation formalism enables one to compute the radiativemoments as nonlinear functionals of the source moments viacanonical moments. Both radiative and canonical moments are of twotypes: Mass type and Current type. The whole idea is to connect the2 radiative moments (U & V ) which the detector sees, via the 2canonical source moments (M & S) to the 6 general ‘source’moments (I , J, W , X , Y , Z ) (last 4 gauge moments)

Computation of the source moments is so far done in the cases ofslow moving, weakly stressed (PN) sources.



In DimReg scheme, Look for soln of EE in D = d + 1 ST dimn withpt pcle matter source (Delta fn in d-dim).. d treated as cx numberand intermediate formulas in PN iteration of the eqns interpreted byanalytical continuation in it by d = 3 + ε. Neglect terms of order εand higher and retain finite part and eventual poles.

(F (x))1 =AC

ε→ 0[

limx→y1

F (x)]

MPM generation formalism enables one to compute the radiativemoments as nonlinear functionals of the source moments viacanonical moments. Both radiative and canonical moments are of twotypes: Mass type and Current type. The whole idea is to connect the2 radiative moments (U & V ) which the detector sees, via the 2canonical source moments (M & S) to the 6 general ‘source’moments (I , J, W , X , Y , Z ) (last 4 gauge moments)Computation of the source moments is so far done in the cases ofslow moving, weakly stressed (PN) sources.


Relation connecting radiative MQ and Source MQBlanchet 92,..98

The relationship between the radiative and source moments involve manynonlinear multipole interactions causing different contributions to the waveformand fluxes.

Uij(U) = I(2)ij (U) +

2GM

c3

∫ +∞

0

dτ

[ln

(cτ

2r0

)+

11

2

]I

(4)ij (U − τ)

+G

c5

{−2

7

∫ +∞

0

dτ I(3)aa(U − τ)

+1

7I

(5)aa − 5

7I

(4)aa −

2

7I

(3)aa +

1

3εabaJb

+4[W (2)Iij −W (1)I

(1)ij

]}+2

(GM

c3

)2 ∫ +∞

0

dτ I(5)ij (U − τ)[

ln2

(cτ

2r0

)+

57

70ln

(cτ

2r0

)+

124627

44100

]+O(7),


FZ flux - Radiative Multipoles

(dEdt

)far−zone

=G

c5

{1

5U

(1)ij U

(1)ij

+1

c2

[1

189U

(1)ijk U

(1)ijk +

16

45V

(1)ij V

(1)ij

]+

1

c4

[1

9072U

(1)ijkmU

(1)ijkm +

1

84V

(1)ijk V

(1)ijk

]+

1

c6

[1

594000U

(1)ijkmnU

(1)ijkmn +

4

14175V

(1)ijkmV

(1)ijkm

]+O(8)

}.

For a given PN order only a finite number of Multipoles contribute

At a given PN order the mass l-multipole is accompanied by the currentl − 1-multipole (Recall EM)

To go to a higher PN order Flux requires new higher order l-multipoles andmore importantly higher PN accuracy in the known multipoles.

3PN Energy flux requires 3PN accurate Mass Quadrupole, 2PN accurateMass Octupole, 2PN accurate Current Quadrupole,........ N Mass 25-pole,Current 24-pole



The Multipolar Post Minkowskian (MPM) formalism developed forBinary Psr work is a good example of the advantage that a completeand mathematically rigorous treatment of a problem can eventuallybring in the future for more demanding applications that could bearound the corner

MPM: Currently the most successful since it can deal with all aspects:the Conservative EOM, Radiation field at infinity, Non-linear efffectsrelated to Tails. Has evolved over the last two decades into aconsistent algorithmic approach to analytical GW computations..Blanchet Liv Rev Rel 9:4 2006; Gravitational Waves - M. Maggiore

3.5PN results for non-spinning ICB on quasi-circular orbitsBlanchet, Damour, BRI, Esposito-Farese, Faye, Arun, Qusailah, Sinha

3PN results for non-spinning ICB on quasi-elliptical orbits(Gopakumar, Arun, Qusailah, Sinha, Blanchet, BRI, Damour, Konigsdorffer, Tessmer)

and 2.5PN results for spinning binaries (Arun, Blanchet, Buonanno, Faye,

Schafer et al, Damour) have recently been completed.


















Basic Inputs - 3PN Energy and 3.5PN Energy Flux x ≡ (πGMF/c3)2/3 ∼ v2

E3(x) = −1

2νx

[1−

(3

4+

1

12ν

)x −

(27

8− 19

8ν +

1

24ν2

)x2

−{

675

64−(

34445

576− 205

96π2

)ν +

155

96ν2 +

35

5184ν3

}x3

],

L =32c5

5Gx5ν2

{1 +

(−1247

336− 35

12ν

)x + 4πx3/2

+

(−44711

9072+

9271

504ν +

65

18ν2

)x2 +

(−8191

672− 535

24ν

)πx5/2

+

(6643739519

69854400+

16π2

3− 1712

105C − 856

105ln(16x)

+

[41π2

48− 134543

7776

]ν − 94403

3024ν2 − 775

324ν3

)x3

+

(−16285

504+

176419

1512ν +

19897

378ν2

)πx7/2 +O(x4)

}Blanchet, BRI, Joguet, Damour, Esposito-Farese


Basic Inputs - 3PN Energy and 3.5PN Energy Flux x ≡ (πGMF/c3)2/3 ∼ v2

E3(x) = −1

2νx

[1−

(3

4+

1

12ν

)x −

(27

8− 19

8ν +

1

24ν2

)x2

−{

675

64−(

34445

576− 205

96π2

)ν +

155

96ν2 +

35

5184ν3

}x3

],

L =32c5

5Gx5ν2

{1 +

(−1247

336− 35

12ν

)x + 4πx3/2

+

(−44711

9072+

9271

504ν +

65

18ν2

)x2 +

(−8191

672− 535

24ν

)πx5/2

+

(6643739519

69854400+

16π2

3− 1712

105C − 856

105ln(16x)

+

[41π2

48− 134543

7776

]ν − 94403

3024ν2 − 775

324ν3

)x3

+

(−16285

504+

176419

1512ν +

19897

378ν2

)πx7/2 +O(x4)

}Blanchet, BRI, Joguet, Damour, Esposito-Farese


3PN GW Flux includes..


Are we there???

Contributions to the accumulated number N = 1π (φISCO − φseismic) of

gravitational-wave cycles. Frequency entering the bandwidth is fseismic =10 Hz; terminal frequency is assumed to be at the Schwarzschildinnermost stable circular orbit fISCO = c3

63/2πGm.

A≡ 2× 1.4M� B≡ 10M� + 1.4M� C≡ 2× 10M�

RR Order A B C

Newtonian 16031 3576 6021PN 441 213 591.5PN −211 −181 −512PN 9.9 9.8 4.12.5PN −12.2 −20.4 −7.53PN 2.6 2.3 2.23.5PN −1.0 −1.9 −0.9

Blanchet, Faye, BRI and JoguetBlanchet, Damour, Esposito-Farese and BRI


Implications of the High accuracy waveforms

High accuracy waveforms underlie construction of GW templates usedin GWDA pipelines of LIGO, Virgo and LISA

Allow one to explore higher mass ranges than with the RWF based onthe dominant harmonic (Arun, BRI, Sathyaprakash, Sinha, van den Broeck, Mishra)

Lead to more accurate parameter extraction accuracy crucial toextract astrophysical info from LIGO and Virgo and cosmological info(like the EOS of Dark Energy) from GW observations of LISA (Arun,

BRI, Sathyaprakash, Sinha, van den Broeck, Mishra)... Implications for Sciencecase of LISA..

Test of GR: Extent to which GW observations of stellar mass BHBand IMBHB by Advanced LIGO and ET and SMBHB by LISA cantest PN Theory (Arun, BRI, Mishra, Qusailah, Sathyaprakash)























Effective-One-Body (EOB)(Buonanno and Damour 98, 00 (2PN),Damour, Jaranowski, Schafer 00 (3PN))

.

Effective-One-Body (EOB) approach - New resummation, to extendvalidity of suitably resummed PN results beyond the LSO, and up tothe merger

At Newtonian approx, the Hamiltonian H0(q,p) can be thought of asdescribing a ‘test particle’ of mass µ orbiting around an ‘externalmass’ GM. (M ≡ m1 + m2 and µ = m1 m2/M);

EOB approach is general relativistic generalization of this. Consists inlooking for an ‘external spacetime geometry’ g ext

µν (xλ; GM) s.t

‘geodesic’ dynamics of ‘test particle’ of mass µ within g extµν (xλ,GM) is

equivalent (when expanded in powers of 1/c2) to original, relativePN-expanded dynamics.

EOB Estimated complete GW signal emitted by inspiralling, plunging,merging and ringing binary black holes



.




µν (xλ; GM) s.t






.




µν (xλ; GM) s.t






.




µν (xλ; GM) s.t






.




µν (xλ; GM) s.t





Effective-One-Body (EOB)

Four essential elements of the EOB approach are:

(i) Hamiltonian Hreal describing conservative part of relative dynamicsof 2 BH

(ii) Radiation-reaction force Fϕ describing loss of (mechanical)angular momentum, and energy, of binary system;

(iii) Definition of various multipolar components of

“inspiral-plus-plunge” (metric) waveform hinsplunge`m ;

(iv) Attachment of subsequent “Ringdown waveform” hringdown`m

around certain (EOB-determined)“merger time” tm.






































Complete Waveform from EOB -Inspiral, Plunge, Merger, Ringdown (Buonanno and Damour, 2000)

.

How Complicated will it be??

−200 −100 0 100t/M

−0.48

−0.38

−0.28

−0.18

−0.08

0.02

0.12

0.22

h(t)

inspiral + plungemerger + ring−downnaive LSOr−LSOj−LSOΕ−LSOω−LSO

ν = 1/4

EOB predicted a blurred transitionfrom inspiral to plunge that is asmooth continuation of inspiral+sharp transition around merger ofcontinued inspiral and ringdownsignal


Complete Waveform from EOB -Inspiral, Plunge, Merger, Ringdown (Buonanno and Damour, 2000)

.

How Complicated will it be??

−200 −100 0 100t/M

−0.48

−0.38

−0.28

−0.18

−0.08

0.02

0.12

0.22

h(t)

inspiral + plungemerger + ring−downnaive LSOr−LSOj−LSOΕ−LSOω−LSO

ν = 1/4

EOB predicted a blurred transitionfrom inspiral to plunge that is asmooth continuation of inspiral+sharp transition around merger ofcontinued inspiral and ringdownsignal


Pretorius and the Numerical Relativity Breakthrough

Pre 2005: Instead of BBH crashes there used to be only code crashes!Dramatic advances in NR allow stable, robust BH merger simulations..

Key Milestones: Initial data for BBH, methods for representing BH oncomputational grids like punctures, importance of hyperbolicity informulating EE for NR, improved formulation of EE, 3D evolutioncodes and use in distorted BH, coord conditions to prevent slices fromcrashing into singularities and spatial coordinates from falling into BHas evolution proceeds, Cactus computational toolkit, modern adaptivemesh refinement finite difference and multi-domain spectralinfrastructure for NR..(Centrella et al RMP 2010)

Pretorius (2005) produced the first simulation with large number oforbits through merger using Mharmonic coords, compactification ofNum Dom at spatial infinity, singularity excision and damping ofconstraints. With this amazing breakthrough in NR, one has reliablewaveforms for the late inspiral and merger parts of the binaryevolution which can be used for constructing templates.












Renaissance of Numerical Relativity with BBH

In 8 months other groups (UTB, NASA GSFC) using other methodslike BSSN eqns and moving puncture methods followed (Equal mass)..

2006: Unequal mass BBH and recoil (Baker et al), Merger ofSpinning BH (Campanelli et al), Long WF [7 orbs] (Baker et al,Buonanno et al), Systematic parameter study (Gonzalez et al) [up to4 orbits before forming common apparent horizon]

Astrophysics implications: Energy in GW, Spin of merged BH, Recoilvelocities of BH and their distribution, EM signatures from finalmerger (BH mergers are expected to be loud; Will they also bebright?? (Centrella et al RMP 2010)

System Energy in GW Final Spin (a/M)f

Non-spinning BBH .04M 0.69Aligned spinning BBH .07M 0.89

Antialigned spinning BBH .02M 0.44

GW Luminosity L ∼ 1023L� greater than total Lum of all stars invisible univ. Stellar BH lasts few millisecs; MBH lasts several mins




















Recoil, Kicks, Superkicks

GW recoil, Kicks: In addition to energy and

AM, GW carry away Linear Mom. Since the

smaller body moves faster its wave emission

undergoes more forward beaming than larger

body. Instantaneously gives net flux of LM

parallel to vel of smaller body and opposite

recoil or kick at CM. Dirn of kick changes as

BH orbit. Since BH is inspiralling instantaneous

kicks do not cancel but accumulate causing

final merged BH to have net recoil in orbital

plane. 100-200 km/sec dep on mass ratio.

Wiseman, Hughes et al

2007 Superkicks - recoils exceeding 1000 km/s (Campanelli et al, Gonzalez et al). Superkicks

possible for spins antialigned and lying in orb plane for equal mass systems and

(a/M)1 = (a/M)2.. Up to 4000 km/s for maxm spinning BH,


Confronting Num Rel with PNA

WF calibrated and interpreted by our PN inspiral results.

There is exciting progress in matching the PN waveforms to theNumerical Relativity ones (Buonanno, Cook, Pretorius 06; Damour, Nagar 06,

Groups at Caltech-Cornell, Goddard, Jena, Rochester, ..)

Baker et al

−1500 −1000 −500 0

−0.2

−0.1

0

0.1

0.2

t/M

Rex

th/M


Confronting Num Rel with PNA

WF calibrated and interpreted by our PN inspiral results.

There is exciting progress in matching the PN waveforms to theNumerical Relativity ones (Buonanno, Cook, Pretorius 06; Damour, Nagar 06,

Groups at Caltech-Cornell, Goddard, Jena, Rochester, ..)

Baker et al

−1500 −1000 −500 0

−0.2

−0.1

0

0.1

0.2

t/M

Rex

th/M


Accurate CB but However...

Provide access to accurate knowledge of the waveform emitted duringlate inspiral and merger (Pretorius 2005; Campanelli et al 2005; Baker et al 2005;

Brugmann et al 2008; Husa et al 2008; Hannam et al 2008; Boyle et al 2007, 2008;

Scheel et al 2009; Vaishnav et al 2007; Hannam et al 2009).

Results available for sparse sample of BBH systems. BBH simulations:time consuming. NR simulations currently too expensive to solelybuild required bank of GW templates and densely fill multidimensionalspace of BBH physical parameters (masses and spins).

Computational cost of accurate equal mass non-spinning 8 orbit BBHsimulation is 200 000 CPU hours. for mass ratio 10 would be at least2 million cpu hours. NR BBH groups require Few million CPU hours

Need for analytical waveforms that represent the best numericalwaveforms - EOB NR; Phenomenological WF..

Improving EOB requires improvement of RR and hence the Waveform




















Improved EOB-based (red) and NR (black)` = m = 2 metric waveforms;Damour and Nagar 2009; Equal-mass case

500 1000 1500 2000 2500 3000 3500 4000

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

t

ℜ[Ψ22

]/ν

Numerical Relativity (Caltech-Cornell)EOB (a5 = 0; a6=-20)

1:1 mass ratio

3800 3820 3840 3860 3880 3900 3920 3940 3960 3980 4000

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

t

Merger time


EOB vs NR - Mass ratio 3:1Buonanno, Pan, Pfeiffer, Scheel, Kidder, Buchman (2009): arXiv: 0902.079

-0.004

-0.002

0

0.002

0.004 Mass ratio 3:1

NR Re(Ψ422) RM

EOB Re(Ψ422) RM

0 200 400 600 800 1000 1200 1400t/M

-0.008

-0.004

0

0.004

0.008

∆A/A: EOB vs. NR(q=3:1, N6)∆φ: EOB vs. NR(q=3:1, N6)∆φ: NR(q=3:1, N5) vs. NR(q=3:1, N6)

The upper panel shows the numerical

and EOB mode Ψ224 , and the lower

panel shows phase and amplitude

differences between EOB and

numerical run. The dashed brown line

is the estimated phase-error of the

numerical simulation, obtained as the

difference between simulations at high

resolution ’N6’ and lower resolution

’N5’.


Other approaches

ADM (Damour, Schafer, Jaranowski), 3.5PN EOM

Direct Integration of Relaxed Einstein Eqns -DIRE (Epstein, Thorne, Will and Wiseman, Pati);2PN EOM and Flux,

Strong field point particle limit (Schutz, Futamase, Asada, Itoh); 3PN EOM.Each star considered as an extended object and limit taken to set radius zeroin a very specific manner. EOM derived by surface integral approach (EIH).

Effective field theory techniques (Goldberger, Porto, Rothstein..) 2PN EOM

Beyond Test pcle: Self-force approaches for EMRI’s...

Beyond PN..Pade Resummation; Effective One Body

Numerical Relativity

NR-AR (Cornell-Caltech, Goddard, Jena, RIT, IHES, Maryland) andSelf force-PN ( Blanchet, Tiec, Whiting, Detweiler...) comparisons....

Phenomenological WF stitching together PN and NR results (Ajith et al)


Overview of comparisons - Blanchet, Detweiler, Tiec, Whiting


Concluding Remarks

Any Experimental Physicist marvels at the audacity of theattempt to detect GW. Detection of GW is nearly impossible.Involves technological challenges that appear insurmountable.That we are close to detecting it is remarkable.When we succeed it will be truely WONDERFUL (Peter Saulson)

Stresses the symbiotic relation between Basic Sciences and AppliedTechnology on one hand and Theory, Experiment, Computation on another..

Experiment driving the theory - PN ICB, Self-force for EMRI, NumericalRelativity, PN-NR comparison.. 2-body problem in GR like Lamb Shift calclnin QED.. But one must keep in mind..

It is not sufficient to transplant in Einstein’s theory thetechnical steps of Newton’s theory but one needs to transmutewithin Einstein’s conceptual framework the ideas thatunderlie the technical developments - Damour


Concluding Remarks






Concluding Remarks






Concluding Remarks






First generation detectors achieve Design sensitivity

Four Hundred years after Galileo’s telescope launched Optical Astronomy,a major revolution in astronomy using GW is around the corner.

Wonderful tribute in the past Year of Astronomy to Galileo from 100’s of braveGW Experimenters struggling over decades believing impossible is nothing!One is left speculating if the first discovery of Gravitational waves would be from

a Binary Black Hole system and Chandra would be doubly right aboutAstronomy being the natural home of General Relativity!!




Wonderful tribute in the past Year of Astronomy to Galileo from 100’s of braveGW Experimenters struggling over decades believing impossible is nothing!

One is left speculating if the first discovery of Gravitational waves would be froma Binary Black Hole system and Chandra would be doubly right aboutAstronomy being the natural home of General Relativity!!




Wonderful tribute in the past Year of Astronomy to Galileo from 100’s of braveGW Experimenters struggling over decades believing impossible is nothing!One is left speculating if the first discovery of Gravitational waves would be from

a Binary Black Hole system and Chandra would be doubly right aboutAstronomy being the natural home of General Relativity!!

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