Astrophysical tests of general relativity in the strong-field regime Emanuele Berti, University of Mississippi/Caltech Texas Symposium, São Paulo, Dec 18 2012 1) 2) 3) 4) What are “strong field” tests? Alternatives to GR: massive scalars BH dynamics and superradiance GWs: SNR and event rates (e)LISA and fundamental physics 5) BH spins and photon mass bounds Coda: Advanced LIGO and astrophysics Strong field: gravitational field vs. curvature; probing vs. testing [Psaltis, Living Reviews in Relativity] Testing general relativity – against what? Finding a contender Action principle Well-posed initial-value problem At most second-order equations of motion Testable predictions! [Clifton+, 1106.2476] Generic scalar-tensor theory Dynamical Chern-Simons Einstein-dilaton-Gauss-Bonnet 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 x - or equivalently large wBD~1/x large mass m>1/R (1AU~10-18eV!) 3) Cosmology “String axiverse”: light axions, 10-33eV < ms < 10-18eV [Arvanitaki++, 0905.4720] Striking astrophysical implications: bosenovas, floating orbits Are massive scalar fields viable? Bounds from: Shapiro time delay: wBD>40,000 [Perivolaropoulos, 0911.3401] Lunar Laser Ranging Binary pulsars: wBD>25,000 [Freire++, 1205.1450] [Alsing, EB, Will & Zaglauer, 1112.4903] Wave scattering in rotating black holes [Arvanitaki+Dubovsky, 1004.3558] Quasinormal modes: Massive scalar field: Ingoing waves at the horizon, outgoing waves at infinity Discrete spectrum of damped exponentials (“ringdown”) [EB++, 0905.2975] Superradiance: black hole bomb when 0 < w < mWH Hydrogen-like, unstable bound states [Detweiler, Zouros+Eardley…] Quasinormal modes In GR, each mode determined uniquely by mass and spin [Visualization: NASA Goddard] 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] f = 1.2 x 10-2 (106Msun)/M Hz 1) Noise S(fQNM) 6M ) s t = 55 M/(10 sun 2) Signal h~E1/2, E=erdM erd~0.01(4h)2 for comparable-mass mergers, h=m1m2/(m1+m2)2 (e)LISA vs. LIGO f = 1.2 x 10-2 (106Msun)/M Hz t = 55 M/(106Msun) s [Schutz; see Sesana’s talk] SNR=h/S: S comparable, h~hM1/2 Ringdown as a probe of SMBH formation 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 [Sesana++, 2012] alar ﬂux at inﬁnity be and comput ed in theinstabilities lowMassive bosoniccan fields superradiant equency regime . For r 0 / M 1 and l = m = 1, Superradiance when w < mWH3/ 2 2 2 1 − µ2 r 3 / M α M s 0 s E˙Any = ∞ light scalar can trigger 12π r 04 a m 2p Θ(Ωp − µs ) , (12) black hole bomb (“bosenova”) here Θ(x) is the Heaviside funct ion. For generic modes, [Yoshino+Kodama, 1203.5070] large distances and for ω = mΩp > µs , scalar raStrongest instability: ation dominates overmgravit sM~1 at ional radiat ion: compare 0705.2880] q. [Dolan, (12) wit h the standard quadrupole formula E˙ ∞g = −5 / 5 (r 0 / M ) m 2p / M 2 . This result is oblivious t o the 10 For m =1eV, M=M : m M~10 sun s BH. In fact, for ω > µs , t he esence s of the rotating Need (orare primordial black holes!) uxes at light the scalars horizon negligible. However, for freencies close t o µflux resonance at superradiant : s , aat Negative scalar the horizonoccurs close to resonances at ωr2es = µ2s − µ2s µs M l + 1+ n 2 , n = 0, 1, ... [Detweiler 1980] (13) Light scalars: floating orbits (Press & Teukolsky 1972) 3 -2 10 -3 10 -2 (mp/M) (dElm/dt) -4 10 -5 10 -6 10 -7 10 -8 s r+ g (dE22/dt) T -(dE11/dt) -4 10 -5 10 -6 10 -7 10 -8 10 -9 10 10 -9 10 -10 10 -11 -2´10 10 -12 10 -13 10 -16 0 Dr0/rres 2´10 -16 -14 10 5 10 15 r0/M 20 25 [Cardoso++ 1109.6021; Yunes++, 1112.3351] complex frequency ω = ωR + i ωI . Physically mo number m are still boundary correspond t o quasinormal Photon bound condit from ions rotating black holes fferent values of mass (pert urbations having ingoing-wave boundary con rotat ion there is a the horizon and outgoing-wave condit ions at rstProca orderperturbations in a ˜ , per- inatKerr [Data points: Brenneman++, 1104.1132] ﬁnity ) and bound states (perturbations t hat a only coupled wit h do not decouple t ially localized wit hin t he vicinity of the BH a milarly t o the case cay exponent ially at null inﬁnity). Here we fo rturbations wit h a Use Kojima’s bound modes, which are expected (based on a oseslow-rotation wit h ± 2 and ﬁeld analogy) t o become superradiantly unsta approximation ωR < mΩH , where ΩH = a ˜ / (2r + ). Our result ons can always be for the ﬁrst time, that massive vect or ﬁelds do ind Stronger instability come unstable when ωR < mΩH . than for massive scalars The bound state modes of t he system (4)–(5) Maximum (again) for found by standard numerical met hods . When 0.1, our numerical results for the fundamental mo msM~1 consistent wit h a hydrogenic spectrum, ωR ∼ µ a A˘ + 2 + O(˜a3 ) , (2) mg<10-20 (or 4x10-21) eV 4 + 5+ 2S M ω ∼ γ (˜ a m − 2r µ) (M µ) , I S + PDG: mg<10-18 eV [Pani++, 1209.0465; 1209.0773] Spin-orbit resonances and spin alignment [Schnittman 04; Kesden++; Lousto’s talk] Can Advanced LIGO reconstruct binary evolution? [Gerosa++, in preparation] Summary 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: wBD>40,000 for ms<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 mg<10-20 (4x10-21eV) (Particle Data Group: mg<10-18eV) [Pani++, 1209.0465; 1209.0773] Advanced LIGO 6) Spin alignment may encode formation history of the binary Effect of tides? Reverse mass ratio?