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about STRONG-FIELD GRAVITY?
University of Arizona
DIMITRIOS PSALTIS
can BLACK HOLES tell us anything
What measures the strength of thegravitational field?
e.g., in the Schwarzschild spacetime
€
g00 = − 1−2GM
rc 2
⎛
⎝ ⎜
⎞
⎠ ⎟dt 2 +
1
1−2GM
rc 2
⎛
⎝ ⎜
⎞
⎠ ⎟dr2 + r2dΩ
potential
€
ε ≡GM
rc 2≈1
the spacetime is far from flat when Gravity is strong (far from
Newtonian) when
What measures the strength of thegravitational field?
In the opposite extreme, what if we add, e.g., a cosmological constant?
€
g00 = − 1−2GM
rc 2+
Λr2
3
⎛
⎝ ⎜
⎞
⎠ ⎟dt 2 +
1
1−2GM
rc 2+
Λr2
3
⎛
⎝ ⎜
⎞
⎠ ⎟
dr2 + r2dΩ
curvature
€
ξ ≡GM
r3c 2≤
Λ
6
Gravity is “weak” when
The Equivalence Principle
€
˙ ̇ x μ +Γρσμ ˙ x ρ ˙ x σ = 0
Newton’s Second Law
€
mI
r ˙ ̇ x =r F G
Einstein’s Equation
€
Rμν −1
2gμν R = 8πTμν
Poisson’s Equation
€
∇2φ = −4πρ
Relativistic Gravity Newtonian Gravity
Newton’s Law of Gravity
€
rF G = −
GmG M
r2ˆ r
The Spacetime Metric
€
ds2 = ...
€
S =1
16πGd 4 x∫ −gR
Einstein’s equation
derived from the Hilbert action:
Ricci curvature
€
R−2Λ( )
Cosmological constant
Gravity is “weak” when
€
R << Λ
€
S =1
16πGd 4 x∫ −gR
How can we extend Einstein’s equation?
higher-order (e.g., R2) Gravity:
€
S =1
16πGd4 x∫ −g R + aR2 + bRμν Rμν + cRαβμν Rαβμν +K( )
Gravity is “strong” when
€
R >>α −1
€
1−E∞
E0
Redshift:
TESTS OF GENERAL RELATIVITYPsaltis 2006
EclipseHulse-Taylor
Mercury
Moon
Neutron StarsGalactic Black Holes
AGN
LIGO
LISAGP-B
Potential (GM/rc2)
€
1−E∞
E0
Redshift:
TESTS OF GENERAL RELATIVITYPsaltis 2006
EclipseHulse-Taylor
Mercury
Moon
Neutron StarsGalactic Black Holes
AGN
GP-B
EW Baryogenesis
Nucleosynthesis
Thorne & Dykla 1971; Hawking 1974; Bekenstein 1974; Sheel et al. 1995
Scalar-Tensor black holes are identical to GR ones!
all R2 terms
any function of R
… in the Palatini formalism
Let’s add:
a dynamical vector field
Psaltis, Perrodin, Dienes, & Mocioiu 2007, PRL, submitted
Always get Kerr Black Holes!!!
We can rely on phenomenological spacetimes
e.g., measure coefficients of multipole expansions of the metric
Ryan 1995; Collins & Hughes 2004
or even measure directly the metric elements from observations
Psaltis 2007
Black holes can be used as null-hypothesis tests against alternativegravity theories that predict massive compact stars
STABLE
UNSTABLE
DeDeo & Psaltis 2003
e.g., in scalar-tensor gravity, neutron stars can be heavy!
=
The Good News
We have a parameter-free solution to an astrophysical problem!
If experiments do not confirm it:
Strong Violation of Equivalence Principle!
Massive Gravitons!!!
Non-local physics!!!!
Berti, Buonanno, Will 2005
e.g., Simon 1990, Adams et al. 2006
Large extra dimensions!!Emparan et al. 2002
log
Tabletop experiments:
€
L < 0.05mm
IN A UNIVERSE WITH LARGE EXTRA DIMENSIONS, BLACK HOLES EVAPORATE VERY FAST DUE TO “HAWKING” RADIATION
EMPARAN et al. 2002
Large Extra Dimensions?
XTE J1118+480
Table Top Limits
Astrophysical Limit: L<0.08mm
Constraining AdS Curvature of Extra DimensionsPsaltis 2007, PRL, in press
CONCLUSIONS
(I) Gravity in the Strong-Field Regime has not been tested
(II) Gravitational Fields of Neutron Stars and Stellar-Mass Black-Holes are the Strongest Found in the Universe a great laboratory to perform gravitational tests
(III) To Learn about Strong-Field Gravity with Black Holes we have to: Resolve the relevant (msec) dynamical timescales Develop a theoretical framework to quantify our results