25
Testing General Relativity With Astrophysical Black Holes University of Arizona DIMITRIOS PSALTIS
Testing General Relativity!With Astrophysical Black Holes!
University of Arizona!DIMITRIOS PSALTIS!
GRAVITATIONAL FIELDS!IN ASTROPHYSICAL SYSTEMS!
Psaltis 2008!
Dark Matter
Dark Energy
Solar System
Stars
White Dwarfs
Neutron Stars
Milky Way
X-ray !Binaries!Intermediate !Mass Black-Holes!
Active Galactic !Nuclei!
Current!tests!
Potential!
Curv
atur
e!
Thorne & Dykla 1971; Hawking 1974; Bekenstein 1974; Sheel et al. 1995 !
Brans-Dicke black holes are identical to GR ones!!
Rabc
d Rab
cd/4
8M2 r
-6
easier said than done because, e.g.,
all R2 terms ! any function of R! … in the Palatini formalism !
Let’s add:!
a dynamical vector field!
Psaltis, Perrodin, Dienes, & Mocioiu 2008, PRL, 100, 091101 !
Uniqueness: Proven so far for (i) Brans-Dicke gravity, (ii) f(R) gravity! (Sotiriou & Faraoni 2012)!
Only known exception: Chern-Simons gravity (Yunes & Pretorious 2009)!
Always get Kerr Black Holes in steady state! !
key point: Vacuum and Black Holes are solutions to the same equation:! Rµν=0!
…an über-No hair theorem!!
Black Holes are Very Simple!!
They are all expected to be described by the Kerr metric, which depends only on two parameters: !
the black-hole mass and its spin!
(no charge in astrophysical black holes)!
A formal test of the no-hair theorem:!
• expand vacuum metric in multipoles!
• use observations to measure at least 3 multipole coefficients !
Ryan 1995; Wex & Kopeikin 1999; Collins & Hughes 2004; Glampedakis & Babak 2006 !Will 2008; Brink 2008; Gair et al. 2008; Apostolatos et al. 2009; Vigeland & Hughes 2010;!
Lukes-Gerakopoylos et al. 2010; Vigeland 2010!
• investigate whether!
€
q = −a2
by writing a general spacetime with!
and measuring the deviation parameter ‘ε’.!
€
q = −(a2 + ε)
The No Hair Theorem: The Kerr solution is the only stationary,!axisymmetric metric in vacuum that has no naked singularities and!no closed timelike loops. !
Black Holes are Very Simple!!
They are all expected to be described by the Kerr metric, which depends only on two parameters: !
the black-hole mass and its spin!
(no charge in astrophysical black holes)!
Regions with pathologies in, e.g., the VH spacetime!
Johannsen, Vigeland, Yunes, Hughes, Psaltis 2012!
A metric that deviates from Kerr, but remains regular !even at very high spins (Johannsen & Psaltis 2011)!
Metrics that deviates from Kerr and are characterized by!Carter-like conserved quantities (Vigeland, Yunes, Stein 2011)!
A census of approaches to testing the No-Hair Theorem!Johannsen, Vigeland, Yunes, Hughes, Psaltis 2012!
Our two golden rules for testing GR with (non-dynamical) observations!of astrophysical objects:!
(i) Look for a phenomenon that has no GR equivalent!
(ii) Perform the same quantitative test with more than one, ! independent probe!
The quadrupole affects: !(i) the location of the Innermost Stable Circular Orbit!
Joha
nnse
n &
Psal
tis (
2010
a)!
GR!
The quadrupole affects: (ii) the amount of gravitational lensing !
Joha
nnse
n &
Psal
tis (
2010
a)!
Sgr A* is the optimal candidate for testing the no-hair theorem!!
Joha
nnse
n et
al.
2012
!
because its horizon has the largest opening angle in the sky!An
gula
r Siz
e of
Sha
dow!
What will the Event Horizon Telescope see?!
Brod
eric
k, J
ohan
nsen
, Psa
ltis,
& L
oeb
2012
!
The Photon Ring: A Ubiquitous Signal, Independent of the Details of the Accretion flow (Johannsen & Psaltis 2011)!
Dext
er e
t al
. 200
9!
Shch
erba
kov
& Pe
nna
2010
!
Mos
cibr
odzk
a et
al.
2009
!
The ring is highly circular for almost all Kerr spins and orientations!
But becomes asymmetric for non-Kerr spacetimes!
A test of the no-hair theorem with Sgr A* images!
Diameter Mass!
Displacement Spin!
Asymmetry Quadrupole!
Any potential violation of the no-hair theorem in Sgr A* can be tested with completely independent observations!
(i) frame-dragging effects in the orbits of IR stars within 1mpc (Will 2008; Merritt et al. 2009)!
GRAVITY!The adaptive optics assisted, beam combiner for the VLTI!
(ii) spin-orbit coupling effects in the timing of an orbiting radio pulsar (Wex & Kopeikin 1998; Liu et al. 2012)!
CONCLUSIONS!
• Measuring the quadrupole moment of the spacetime of a! black hole leads to a quantitative, formal test of the no-hair theorem!
• Observations of Sgr A* may lead to the first ! test of the no-hair theorem in the near future with:! (i) high-resolution images of its shadow! (ii) dynamical measurements with orbiting stars! (iii) dynamical measurements with radio pulsars!
• The Event Horizon Telescope and GRAVITY are opening a new ! window in gravitational physics!
• A well developed theoretical framework exists for performing! this test!
