From prediction to detection:Highlights of the fascinating

history of Gravitational Waves

Bala IyerICTS-TIFR, Bangalore, India

IndIGO Consortium

IndIGOIndian Initiative in Gravitational-wave Observations

Indian Academy of Science MYMIISc, 1 July 2016

Track OneAnalytical RelativityBirth of Relativistic

Astrophysics

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General RelativityEinstein’s Relativistic Gravity

Epitome of Mathematical elegance, Conceptual depth, Observational success

25 Nov 2015: Centenary of General Relativity

~

credit: www.chicagonow.com

Einstein's view: Gravitation

~ Spacetime Geometry ~ Curvature or Distortion

of Spacetime

Einstein’s Eqns10 coupled

nonlinear PDE

Far Reaching Impact• GR can be applied to universe as a whole leading to

Modern Cosmology dealing with origin, evolution andend of the universe..

• Extreme warping of space-time: Existence ofNeutron stars (3 Msun mass limit) and Black holes.

• Prediction of Gravitational waves crowned by the First Detections

• Precision Cosmology with observations of CMB• Relativistic Astrophysics:

Observations of pulsars, quasars, x-ray sources• Heralds the dawn of a New

Transformative Astronomy

Gravitational Waves• 1916: Using Linearized gravity Einstein

proposed existence of GW as one of General Relativity’s important consequence

• 1918: Einstein calculated flux of energy far from source.. Quadrupole Formula..

• Radiation Reaction ..Radiation Damping. Energy carrying waves vs non-energy carrying wave-like coordinate artefacts..

• 1922: Eddington: Pointed inapplicability of AE's derivation for self gravitating systems. Realized issues of gauge effects subtle : GW propagate at speed of thought! 6Complication for a self-gravitating system

h Newton

c2v2

c2=GmRc2

v2

c2

Gravitational Waves do not exist!

• Subtleties continued to vex even Einstein• 1936: Einstein to Born..

• “Together with a young collaborator (Rosen), I arrived at the interesting result that GW do not

exist, ...." • Convinced about his erroneous interpretation

and retracted in the published paper saying: "fundamental" changes in the paper were

required because "consequences" of the Eqnsderived in the paper had previously been

incorrectly inferred.

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Complication for a self-gravitating system

Post Newtonian Approximation• 1916: To calculate (v/c) relativistic corrections to

Newton, Einstein, Droste, De Sitter introduced Post Newtonian (PN) approximation method .

• Combines 3 different expansions: weak-field, slow-motion and near-zone expansion

• 1PN (v2/c2) corrections to Newtonian Gravity approximation for describing the dynamics of N extended bodies had difficulties in treatments of the internal structures of the bodies.

• 1938 Einstein, Infeld and Hoffmann (EIH) – GR N-body problem reached first stage of maturity. Books of Fock, Infeld & Plebanski, Landau & Lifshiftz

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Self-gravitating system• Complication: For self-gravitating systems orders

in velocity are related to orders in non linearity.. By Virial theorem φ =GM/R same order as v2..

• Reaction terms of order (v/c)5 in linear theory will be accompanied by terms (v/c)3 φ/ c2, (v/c)(φ/c2) 2..

for self-gravitating systems• Higher order PN calculation requires dealing

dealing with higher order non-linearities of Einstein's Equations.

• Landau Lifshiftz (1941) and Fock (1955) extended Quadrupole formula to weakly self-gravitating systems.. Constitute two different approaches to GW generation today.. DIRE vs MPM-PN 9

The Babel

• Many inconsistent results which today we cantrace to: Issues related to coordinate vsphysical singularities, use of retarded vsadvanced potentials or combination, No-incoming BC in a PN scheme…

• (Ritz, Tetrode, Infeld, Rosen, Hu,Scheidegger, Goldberg, Havas, Peres,Trautman, Burke-Thorne …..)

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Chandrasekhar and GW • 1960's: Chandrasekhar - Radiation Reaction

problem.. How does emission of GW affect theemitting system when its self-gravitating?

• First to show conceptually that radiation reactionproblem could be solved. Assembled together theessential ingredients: Landau-Lifshiftz pseudo-tensor to include the non-linearities of the Grav field,Retarded potentials and near-zone expansion toimplement outgoing BC following Trautman.

• Gave astrophysicists confidence that GR wasphysically reasonable and well behaved. Energyand AM radiated as GW was correctly balanced bythe loss of mechanical energy and AM.

• ) GW GR Centenary August11

Black Holes• 1916: First Exact Soln of EE: Schwarzschild• 1939: Oppenheimer and Snyder showed Sph. Symm

collapse of dust due to gravitational self-attraction leads toAp. BH. BH not considered physical due to idealizations ofSS and dust

• 1960s: Nature of Schwarzschild singularity atR=2GM/c2 understood by the work of Finkelstein,Kruskal. Global methods of Penrose, Hawking,

• Notion of Event horizon. Schwarzschild Black hole.• 1963: Kerr Solution. Rotating Black hole

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Schwarzschild Oppenheimer Snyder

Kerr

Volkov

Penrose Hawking

Black Holes

• BH Perturbations (Regge, Wheeler, Teukolsky)

• 1970 - Vishveshwara• Linear Stability, Quasi normal modes of BH• Innermost stable circular orbit R= 6 G M/c2; • Light Ring: R=3 G M/c2

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Track TwoPhysical effect of GW

And how we can measure them

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Felix Pirani Hermann Bondi

GR1 - Chapel Hill - 1957• 1957: Conference on role of Gravitation in

Physics Chapel Hill - GR1 • GW problem was solved and Quest for

GW detection born• Pirani: Focus on and Analyse effect of

GW rather than generation of GW. • Effect of GW determined by Eqn of

Geodesic deviation. In presence of GW a set of FF masses would experience genuine motion relative to each other. Thus GW were real.

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GR1 - Chapel Hill - 1957• Bondi asks: Can U connect two masses with a

dashpot thus absorbing energy from the wave.• Pirani replies: I have not put an absorption

term but put in a spring. U can invent a system with such a term quickly..

• Bondi credited with sticky bead argument.

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• Tidal motion of particles due to GW generates heat by the

rubbing of particles against the rod! GW could in principle heat a suitably contrived mechanical

system!

GW are Physical • GW can be made to do all sorts of strange things by

choice of coordinates, but the way they interact with matter must always make sense physically.

• 1962: Far from the source, using null coordinates andthe Weyl tensor, "Bondi News" (derivative of shear) isrelated to mass loss providing a coordinate invariantcharacterization of GW.. (Pirani, Bondi, Metzner, Sachs,Goldberg, Newman..).

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A ring of particles would be tidally stretched and squeezed in a

oscillatory time dependent manner

if GW incident normally on it

Joe Weber: Tragic Pioneer• Weber and Wheeler were at Chapel Hill • 1960 Weber Bar idea• Confidence in physicality of GW. Weber

began GW detection when theory of the subject was in disarray, disabling!

• 1969 Weber's first claim of GWdetection; coincident excitationsof bars at Aragone Natl Lab and Univ of Maryland coming from galactic centre.

• 1972+:Other groups failed to replicate Weber's results (Braginsky, Tyson, Drever, Garwin and Levine,..)

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Laser Interferometers for GW detection• 1963 Gerstenstein and Pustovit: Laser interferometry to

detect GW• 1964: Rai Weiss (MIT) - While teaching GR asked:

What is measurable in GR? Found the answer in Pirani, who had not put spring or dashpot but said: It is assumed that an observer by use of light signals or otherwise determines the coordinates of a neighbouring particle in his local cartesiancoordinate system.

• 1972: Rai Weiss's instruction book.. HW problem.. Rai envisions LIGO

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Laser Interferometers for GW detection

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• As a GW from a NS-NS binary in Virgo cluster passes, the arm lengths of km scale IFO change (10 -18m) tidally causing the interference pattern to change at the photodiode.

• GW detection is about seeing the biggest things that ever happen by measuring the smallest changes that have ever

been measured - Harry Collins.

Reference Documents Slide Credit Stan Whitcomb

Three documents central to the technical history of LIGO• “Rai’s RLE paper”

» “Electromagnetically Coupled Broadband Gravitational Antenna”» R. Weiss, Quarterly Reports of the Research Laboratory of Electronics

MIT 105, p. 54 (1973).» Paper “… grew out of an undergraduate seminar that I ran at M.I.T.

several years ago…”

• The “Blue Book”» “A Study of a Long Baseline Gravitational Wave Antenna System”» Authors: Paul Linsay, Peter Saulson, Rai Weiss» Dated October 1983, but not really published

• NSF Proposal for LIGO Construction (’89 proposal)» Proposal team: Robbie Vogt, Ron Drever, Rai Weiss, Kip Thorne, Fred

Raab, but with contributions from many others

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RLE PaperSlide credit: Stan Whitcomb

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First detailed noise/ sensitivity analysis» Shot noise/

radiation pressure» Thermal noise» Seismic noise» Gravity gradient» …

Gerstenstein & Pustovoit; Forward, Billing and Winkler, Meers..

Ray Weiss

Kip Thorne Kip Thorne Alain Brillet AdalbertoGiazotto

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Ray Weiss Ron Drever

Track ThreeDiscovery of the Binary Pulsar

High quality data ≈ Proof that GW exist

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Binary Pulsar B1913+16 • 1974 Hulse and Taylor Discovered the Binary

Pulsar 1913+16

• If General relativity is right the system must emit GW and inspiral inwards

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Orbital period slowly decreasing at just

the rate predicted by GR for emission of GW!!! Indeed, Orbit

shrinks by 3 mm/orbit..

Quadrupole Formula controversy to Mark II Approximation methods

• Prospects of testing PN theory against Hulse-Taylor system once again revived more criticalquestions regarding existing treatment of GW.Forced a revisit to approximation methods in GR toremedy mathematical shortcomings in the existingapproaches. Led to MPM-PN

• Mandated improved approaches to the 2-bodyproblem: Modern versions of EIH to obtain:a = aNewton + a1PN + a2PN + a2:5PN

• (1980's,early 90's Ohta, Okamura, Kimura, Hiida; Bel et al, Damour-Deruelle, Damour; Futamase and Schutz; Walker-Will; Grischuk Kopeijkin, Haridass & Soni. Kip Thorne's 1980 Rev. Mod. Phys. State of the art in techniques involved and results then available)

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Insights into GR and GW from Binary Pulsars

• Binary pulsars like 1913+16 provide direct observationalproof that gravity propagates at velocity of light and has aquadrupolar structure

• GR valid beyond quasi-stationary weak-field regime.Probed for first time in regimes involving radiative effectsand strong fields. GR passed all binary pulsar tests withflying colors

• Existence of binary neutron stars emitting GW forhundreds of million years before coalescing spectacularlyin sensitivity BW of detectors like LIGO/Virgo

• Binary Pulsar population underlay the estimated numberof GW events for Laser Interferometric GW detectors.

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Track FourTowards Direct Detection of

Gravitational Waves

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The Last three minutes..Coalescing Compact Binaries

¾ Late Inspiral and Merger Epochs of compactbinaries of neutron stars or black holes provide uspossible strong sources of GW for LIGO and Virgoin the `high' frequency range 10 Hz - 10 kHzNote …. v/c ~ .4 ..Highly Relativistic..

¾ We have guaranteed sources for the GW detectorsif there are enough of them. The waveform is aCHIRP : Amplitude and Frequency increasing withTime

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Matched Filtering, Source Modelling¾ GW are WEAK SIGNALS buried in LARGE NOISE of

detector¾ Require Matched Filtering (MF) both for their

Detection or Extraction and Parameter Estimationor Characterisation

¾ Success of MF requires Accurate model ofsignal using GR.

¾ Favours sources like Coalescing Compact Binaries(CCB) [NS-NS, BH-BH, NS-BH] over unmodelledsources like supernovae. Expt Needed and Led toProgress in 2-body problem in GR much beyondBinary Pulsar case …

¾ 1990+: Indian Legacy in GW research in groups atIUCAA on Data Analyses (Dhurandhar) and RRI onSource modelling (BI) 32

Last three minutes – Cutler et al • When LIGO was funded in early nineties, and efforts to

construct accurate CCB waveforms for NS-NS, BH-BHstarted, it was soon realised that far higher order PN accuratewaveforms would be needed to accurately describe GW inthe final stages of inspiral and merger ( v/c ~ .2, GM/(R c2)~.2) than the 2.5PN adequate for Binary Psr work ( v/c ~ 10-

3, GM/ (R c2) ~ 10-6). CCB were highly relativistic at these lateepochs

• Physical insights were essential to simplify the goals and achieve the required accuracy for waveforms to construct template banks.. They include: Quasi-circular motion near merger, Priority to modelling Phase rather than amplitude, Adiabatic approximation modelling inspiral as motion from a circular orbit to next, Modelling binaries as point particles using Delta functions. Self field Regularization

• Multipolar Post Minkowskian - Post Newtonian Method33

Figure Credit: Thorne

Effective-One-Body (EOB)Buonanno, Damour (1999, 2000)

• Starting point: High order PN and perturbation theoryresults guided by the insight that non-perturbative effectscan be captured analytically if key ingredients that enterthe two body dynamics and GW emission are properlyresummed about the exact test particle results

• Basic idea is to first construct an auxiliary effectivedescription of real conservative dynamics in which aneffective particle of mass M and effective spin S movesin a deformed Kerr-like geometry g(M;S) s.t.conservative dynamics is equivalent (when expanded inpowers of 1/c2) to original, relative PN-expandeddynamics. Supplement by Radiation reaction forcecomputed from a inspiral-merger waveform and attach toa Ringdown QNM around merger time.

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(Buonanno, Damour 2000)

Pretorius &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..

• Pretorius (2005) produced the first simulationwith large number of orbits through merger usingModified harmonic coords, compactification ofNum Dom at spatial infinity, singularity excisionand damping of constraints.

• 2006: Campanelli et al, Baker et al• With this amazing breakthrough in NR, one has reliable

waveforms for the late inspiral and merger parts of thebinary evolution which can be used for constructingtemplates. 40

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Baker et al (2006)

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Post Newtonian -Æ Effective One Body/Phenomenological (Ajith et al + ) ÅÆNumerical Relativity

EXQUISITE THEORY

The Data Analysis Infrastructure• Using Best Waveform models construct Template

Banks and efficiently cover the parameter spaceto be explored ( masses, spins) for detection firstand parameter estimation later.

• Group around Sanjeev Dhurandhar at InterUniversity Centre for Astronomy andAstrophysics (IUCAA) contributed significantly toGW Data Analysis since 1990

• SPA, template placement, hierarchical strategy,parameter estimation, radiometer searchmethods, detector characterization, CW searchstrategies

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The unforgiving experiment

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Pre-stabilized LaserActive Seismic Isolation

‘TransMon’ Telescope

Output Mode Cleaner ‘Test Mass’ Mirror

Credit: D. Reitze

And at last … • With Advanced LIGO, we achieved the

technology to make a direct detection ofgravitational waves 100 years after Einsteinpredicted them.

• We also have corresponding progress in the twobody problem in general relativity to detectGW, characterize them and begin to testgeneral relativity

• From the NS binaries justifying our proposal(known-knowns), to the discovery of the BHbinaries at our first detection (known-unknowns), one is now left speculating aboutthe possibilities GW astronomy may reveal(unknown unknowns) 45

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Was the 1919 of our generation.What more would Einstein want at the centenary of GR, GW, BH??

Feb 11 2016