1. Astrophysical tests of general relativity in the strong-field regime Emanuele Berti, University of Mississippi/Caltech Texas Symposium, São Paulo, Dec 18 2012

2. 1)What are “strong field” tests? 2)Alternatives to GR: massive scalars 3)BH dynamics and superradiance 4)GWs: SNR and event rates (e)LISA and fundamental physics 5)BH spins and photon mass bounds Coda: Advanced LIGO and astrophysics

3. Strong field: gravitational field vs. curvature; probing vs. testing [Psaltis, Living Reviews in Relativity]

4. Testing general relativity – against what?

5. Finding a contender Action principle Well-posed initial-value problem At most second-order equations of motion Testable predictions! Dynamical Chern-Simons Einstein-dilaton-Gauss-Bonnet Generic scalar-tensor theory [Clifton+, 1106.2476]

6. A promising opponent: massive scalar fields 1) Phenomenology  Modern equivalent of planets [Bertschinger]  Well-posed, flexible (Damour & Esposito-Farése “spontaneous scalarization”)  f(R) and other theories equivalent to scalar-tensor theories 2) High-energy physics  Standard Model extensions predict massive scalar fields (dilaton, axions, moduli…)  Not seen yet: dynamics must be frozen small coupling  - or equivalently large  BD  1/  large mass m>1/R (1AU  10 -18 eV!) 3) Cosmology  “String axiverse”: light axions, 10 -33 eV < m s < 10 -18 eV [Arvanitaki++, 0905.4720] Striking astrophysical implications: bosenovas, floating orbits

7. Are massive scalar fields viable? Bounds from: Shapiro time delay:  BD >40,000 [Perivolaropoulos, 0911.3401] Lunar Laser Ranging Binary pulsars:  BD >25,000 [Freire++, 1205.1450] [Alsing, EB, Will & Zaglauer, 1112.4903]

8. Wave scattering in rotating black holes Quasinormal modes:  Ingoing waves at the horizon, outgoing waves at infinity  Discrete spectrum of damped exponentials (“ringdown”) [EB++, 0905.2975] Massive scalar field:  Superradiance: black hole bomb when 0 <  < m  H  Hydrogen-like, unstable bound states [Detweiler, Zouros+Eardley…] [Arvanitaki+Dubovsky, 1004.3558]

9. f = 1.2 x 10 -2 (10 6 M sun )/M Hz  = 55 M/(10 6 M sun ) s  In GR, each mode determined uniquely by mass and spin  One mode: (M,a) Any other mode frequency: No-hair theorem test  Relative mode amplitudes: pre-merger parameters [Kamaretsos++,Gossan++]  Feasibility depends on SNR: Need SNR>30 [EB++, 2005/07] 1) Noise S(f QNM ) 2) Signal h  E 1/2, E=  rd M  rd  0.01(4  ) 2 for comparable-mass mergers,  =m 1 m 2 /(m 1 +m 2 ) 2 Quasinormal modes [Visualization: NASA Goddard]

10. (e)LISA vs. LIGO [Schutz; see Sesana’s talk] SNR=h/S: S comparable, h  M 1/2 f = 1.2 x 10 -2 (10 6 M sun )/M Hz  = 55 M/(10 6 M sun ) s

11.  LISA/eLISA studies: merger-tree models of SMBH formation  Light or heavy seeds? Coherent or chaotic accretion? [Arun++, 0811.1011]  eLISA can easily tell whether seeds are light or heavy [Sesana++, 1011.5893]  Mergers: a  0.7 Chaotic accretion: a  0 Coherent accretion: a  1 [EB+Volonteri, 0802.0025]  >10 binaries can be used for no-hair tests  Spin observations constrain SMBH formation Ringdown as a probe of SMBH formation [Sesana++, 2012]

12. Massive bosonic fields and superradiant instabilities Superradiance when  < m  H Any light scalar can trigger a black hole bomb (“bosenova”) [Yoshino+Kodama, 1203.5070] Strongest instability:  s M  1 [Dolan, 0705.2880] For  s =1eV, M=M sun :  s M  10 10 Need light scalars (or primordial black holes!) Negative scalar flux at the horizon close to superradiant resonances at [Detweiler 1980]

13. Light scalars: floating orbits (Press & Teukolsky 1972) [Cardoso++ 1109.6021; Yunes++, 1112.3351]

14. Photon mass bound from rotating black holes Proca perturbations in Kerr do not decouple Use Kojima’s slow-rotation approximation Stronger instability than for massive scalars Maximum (again) for  s M  1 m  <10 -20 (or 4x10 -21 ) eV PDG: m  <10 -18 eV [Pani++, 1209.0465; 1209.0773] [Data points: Brenneman++, 1104.1132]

15. [Schnittman 04; Kesden++; Lousto’s talk] Spin-orbit resonances and spin alignment

16. Can Advanced LIGO reconstruct binary evolution? [Gerosa++, in preparation]

17. Tests within GR 1)(e)LISA: Tens of events could allow us to test the no-hair theorem Advanced LIGO/ET can also test no-hair theorem - if IMBHs exist! 2)Spin measurements constrain SMBH merger/accretion history [EB++, 0905.2975; EB+Volonteri, 0802.0025] Massive bosons and superradiant instabilities 3)Weak-field: Solar System, binary pulsars Cassini:  BD >40,000 for m s <2.5x10 -20 eV Binary pulsars will do better in a few years [Alsing++, 1112.4903; Horbatsch++, in preparation] 4)Massive scalars: floating orbits [Cardoso++, 1109.6021; Yunes++, 1112.3351] 5)Massive vectors and SMBH spins: best bounds on photon mass m  <10 -20 (4x10 -21 eV) (Particle Data Group: m  <10 -18 eV) [Pani++, 1209.0465; 1209.0773] Advanced LIGO 6)Spin alignment may encode formation history of the binary Effect of tides? Reverse mass ratio? Summary