The Cosmic Barber: Counting Gravitational Hair in the Solar System and beyond. Clifford Will Washington University, St. Louis

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1 The Cosmic Barber: Counting Gravitational Hair in the Solar System and beyond Clifford Will Washington University, St. Louis Testing GR with Astrophysical Systems May 17, 2012

2 Counting Gravitational Hair The 3 Stooges: Moe, Curly & Larry ( )

3 The Cosmic Barber: Counting Gravitational Hair in the Solar System and beyond Introduction - what is hair? Counting scalar hair in the solar system Counting Earth s Newtonian hair with GRACE Counting Earth s J-hair o Gravity Probe B o LAGEOS Counting hair at the galactic center Testing GR with Astrophysical Systems, May 17, 2012

4 External potentials of charge and mass distributions Electromagnetism (axisymmetric body) A i : : e r i r 2 DP 1 (cos ) Q 2 P 2 (cos ) r 2 r 3 M 2 P i 2 (cos ) r 3 Newtonian gravity (axisymmetric body) U : M r Q MR j Q 2 P 2 (cos ) Q 3 P 3 (cos ) r 3 r 4 Earth: j 2 = X 10-4, j 3 = 9.6 X 10-7, j 4 = 5.4 X 10-7,

5 General relativistic hair Exterior geometry any stationary, axisymmetric body: g 00 : M Q 2 P 2 (cos ) Q 3 P 3 (cos ) r r 3 r 4 g 0 : J J 2 P 2 (cos ) J 3 P 3 (cos ) r 2 r 3 Black holes have no hair r 4 Q ij M(ia) Hansen 1974 Q 2 Ma 2 J 2 /M Q 0 J 1 a J M J / M

6 Scalar hair In scalar-tensor theories of gravity: g 00 : M T r M S M K r M K M T g ij : rr M S M T M T M S M S For non-relativistic bodies M S M T 1 2

7 Penrose (1970) - conjecture at 5th Texas Symposium Thorne & Dykla (1971) - scalar field radiated away, in accord with Price s theorem Hawking (1972) - stationary, vacuum black holes in BD = GR black holes CMW (1981) - BBH the same at 1PN order Sotiriou & Faraoni (2011) - extended Hawking theorem to general ST & f(r) theories Mirshekari & CMW (2012) - BBH the same at 2.5PN order Black holes have no scalar hair Basic idea: scalar field outside black holes must be constant (M S =0)

8 Binary Black Holes: Are the Scalar- Tensor and General Relativistic Conjecture 2.0: Versions Indistinguishable? Following an initial transient period << the orbital period, the orbital evolution and gravitational radiation from BBH in ST theory* are identical to those predicted by GR, after a mass rescaling, independent of the initial scalar field configuration *Assumptions 1. Scalar-tensor theory with no potential 2. Vacuum asymptotically flat spacetime 3. Asymptotic constant in time 4. 2 black holes with non-singular event horizons

9 The Cosmic Barber: Counting Gravitational Hair in the Solar System and beyond Introduction - what is hair? Counting scalar hair in the solar system Counting Earth s Newtonian hair with GRACE Counting Earth s J-hair o Gravity Probe B o LAGEOS Counting hair at the galactic center Testing GR with Astrophysical Systems, May 17, 2012

10 Bounding the scalar hair of the sun M S M T 10 5

11 The Cosmic Barber: Counting Gravitational Hair in the Solar System and beyond Introduction - what is hair? Counting scalar hair in the solar system Counting Earth s Newtonian hair with GRACE Counting Earth s J-hair o Gravity Probe B o LAGEOS Counting hair at the galactic center Testing GR with Astrophysical Systems, May 17, 2012

12 Measuring the Earth s Newtonian hair Gravity Recovery And Climate Experiment (GRACE) Earth: j (5) X = X 10, j (1) X = 9.6 X 10-7, j (4) X = 5.4 X 10-7, j 360 = 3.2 (5) X 10-10

13 The Cosmic Barber: Counting Gravitational Hair in the Solar System and beyond Introduction - what is hair? Counting scalar hair in the solar system Counting Earth s Newtonian hair with GRACE Counting Earth s J-hair o Gravity Probe B o LAGEOS Counting hair at the galactic center Testing GR with Astrophysical Systems, May 17, 2012

14 Gravity Probe B: Measuring Earth s J Launch April 20, 2004 Mission ended Sept 2005 Result announced May

15 Gravity Probe B: The Experiment -- Gyroscopes Disclosure: CMW chaired NASA s Science Advisory Committee for GPB ( )

16 Gravity Probe B: The final science result The main error source Patch effect misalignment torques

17 Gravity Probe B: The final science result Measured Predicted Geodetic Precession (mas) Frame-Dragging (mas) 6602 ± ±

18 LAGEOS: Measuring Earth s J NewEarth models from GRACE are essential

19 The Cosmic Barber: Counting Gravitational Hair in the Solar System and beyond Introduction - what is hair? Counting scalar hair in the solar system Counting Earth s Newtonian hair with GRACE Counting Earth s J-hair o Gravity Probe B o LAGEOS Counting hair at the galactic center Testing GR with Astrophysical Systems, May 17, 2012

20 Counting hair on the galactic center black hole SgrA* No hair theorems: M L + ij L = M(ia) L J = Ma; Q = -Ma 2 relativistic effects: periholion advance, redshift Doppler shifts, Shapiro delays Frame dragging (J) and quadrupole moment (Q) produce precessions of planes

21 Using Orbit plane precessions to count the hair on SgrA* i M J * A M 6 A J 4 M a (1 e 2 ) J M 2 M a (1 e 2 ) 3 / 2 Q dirt A Q 3 Q M 3 M a (1 e 2 ) 2 a/m > 0.5 P ~ 0.1 yr, d < 10-3 pc, e ~ 0.9 => Precessions ~ 10 as/yr CMW, Ap J Lett. 647, L25 (2008)

22 The observational challenge 4 mpc GRAVITY: near IR adaptive optics instrument for the Very Large Telescope Interferometer 1 mpc.1 mpc QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture. ASTRA: extending the Keck interferometer

23 Effect of other stars/bh in the central mpc 10 stars (1M o ) & 11 BH (10M o ) within 4 mpc 100 realizations isotropic, mass segregated J/M 2 = 1 Numerical N-body simulations: D. Merritt, T. Alexander, S. Mikkola, & CMW, PRD 81, (2010) Analytic orbit perturbation theory: L. Sadeghian & CMW, CQG 28, (2011)

24 The Cosmic Barber: Counting Gravitational Hair in the Solar System and beyond Introduction - what is hair? Counting scalar hair in the solar system Counting Earth s Newtonian hair with GRACE Counting Earth s J-hair o Gravity Probe B o LAGEOS Counting hair at the galactic center Testing GR with Astrophysical Systems, May 17, 2012

25 The Cosmic Barber: Counting Gravitational Hair in the Solar System and beyond Coming Fall 2012 Clifford Will University of Florida, Gainesville Testing GR with Astrophysical Systems May 17, 2012

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