and STRONG-FIELD GRAVITY

University of Arizona

DIMITRIOS PSALTIS

BLACK HOLES

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 = ...

Where does Einstein’s equation come from?

€

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?

When did this happen?

Mirabel et al. 2001

XTE J1118+480

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