Black-hole binaries in Einstein-dilaton Gauss–Bonnet gravity Helvi Witek Theoretical Particle Physics and Cosmology Department of Physics, King’s College London work in progress with L. Gualtieri, P. Pani, T. Sotiriou Workshop: “Gravity and cosmology 2018”, YITP Kyoto, 6 February 2018 H. Witek (KCL) 1 / 16
Why challenging general relativity? Cosmology • observational evidence for dark matter/energy • cosmological constant problem • evolution of the universe High-energy physics • general relativity is non-renormalizable • UV completion and quantum gravity? • curvature singularities H. Witek (KCL) 2 / 16
A need for theoretical predictions. . . GR very well tested, e.g. on solar system scales, with binary pulsars, with gravitational waves from black holes and neutron stars BUT: in merger regime only null tests!!! • very few theoretical predictions in extensions of GR (scalar-tensor theory [Healy et al ’11, Berti ’13, Barausse et al ’12, Shibata et al ’13], dynamical Chern-Simons [Okounkova et al ’17]) • needed to calibrate parametrized models, e.g., extensions of EoB, ppN, ppE, . . . • no parametrized numerical models → choose most promising candidates (credit: LIGO / Virgo Scientific Collaborations) H. Witek (KCL) 3 / 16
Here: Einstein-dilaton Gauss-Bonnet gravity action of EdGB gravity (e.g. Kanti et al ’95) d 4 x √− g � � S = 1 � (4) R + α GB f (Φ) R GB − 1 2( ∇ Φ) 2 16 π • R GB = R 2 − 4 R ab R ab + R abcd R abcd G ab =8 π T Φ ab − 16 πα GB G GB ab , • typically: f (Φ) ∼ e Φ � Φ = − α GB f ′ (Φ) R GB 1 1 use geometric units c = 1 = G H. Witek (KCL) 4 / 16
Why EdGB gravity? High-energy physics • higher curvature corrections relevant in strong-curvature regime • low-energy limit of some string theories (Gross & Sloan ’87, Kanti et al ’95, Moura & Schiappa 06) • compactification of Lovelock gravity (Charmousis ’14) H. Witek (KCL) 5 / 16
Why EdGB gravity? – musings on compact objects • in standard scalar-tensor theory: • BUT: reverse in quadratic gravity! • no-hair theorems for BHs • BHs can have hair! (Bekenstein ’95, Heusler ’96, Sotiriou & Faraoni ’11) (Hui & Nicolis ’12, Sotiriou & Zhou ’14) • neutron stars can have scalar hair • monopole scalar charge for neutron star vanishes (Yagi et al ’15) (Damour & Esposito-Farese ’93, ’96, . . . ) J • rotating black holes with χ = M 2 in small coupling approximation (Kanti et al ’95, Pani et ’09, ’11, Stein & Yunes ’11, Sotiriou & Zhou ’14, Ayzenberg & Yunes ’14, Maselli et al ’15, Kleihaus et al ’11, ’14, . . . ) • α 0 GB : no modification to GR solution, i.e., d s 2 = d s 2 a/M = 0.7, num Kerr , Φ = const = 0 a/M = 0.7, ana a/M = 0.9, num a/M = 0.9, ana 1 a/M = 0.99, num a/M = 0.99, ana • α 1 GB : no modification to metric, but scalar hair 0.1 Φ (courtesy of Kent Yagi) 0.01 M l +1 � � M �� � Φ = r l +1 P l (cos θ ) 1 + O P l r 0.001 1 10 100 l ≥ 0 , even x / M � 1 − χ 2 − 1 + χ 2 1 − 5 χ 2 P 0 =4 α GB P 2 ∼ − 28 α GB � � M 2 χ 2 + O ( χ 6 ) M 2 χ 2 15 98 H. Witek (KCL) 6 / 16
Why EdGB gravity? – musings on compact binaries ⇒ modified dynamics and extra polarizations, e.g, • induced scalar dipole & quadrupolar radiation ⇒ increased inspiral rate • shift in binding energy ⇒ correction to orbital phase • change in ISCO: r ISCO / M ∼ 6 − 16297 9720 α 2 GB • spin can exceed Kerr bound (Kleihaus et al ’11) • . . . (www.eventhorizontelescope.org) H. Witek (KCL) 7 / 16
Setting the stage for numerical evolutions Mathematical considerations: • field equations are second order ⇒ potential for well-posed PDE system? • in generalized harmonic gauge only weakly hyperbolic (Papallo & Reall ’17, Papallo ’17) • extension to Baumgarte-Shapiro-Shibata-Nakamura-type formulation + puncture-type gauge underway (work in progress with L. Gualtieri and P. Pani) • good chances as effective field theory (Choquet-Bruhat ’88, Delsate et al ’14) g µν = g (0) µν + ǫ g (1) µν + O ( ǫ 2 ), Φ = ǫ Φ (1) + O ( ǫ 2 ) and take ǫ ∼ α GB • G (0) α 0 GB : ab =0 , � Φ (1) = −R (0) GB = R 2 − 4 R ab R ab + R abcd R abcd R (0) α 1 GB : GB , ⇒ in practise for up to α 1 GB : evolve scalar in a GR background H. Witek (KCL) 8 / 16
BH binaries in EdGB – setting the stage Time evolution in 3+1 dimensions, code based on Einstein Toolkit Initial data: • α 0 GB : non-spinning BH binary with x ± = ± 5 ( ∼ 8 − 10 orbits before merger), mass-ratios q = m 1 / m 2 = 1 , 1 / 2 , 1 / 4 • α 1 GB : zero initial scalar field or superposition of solutions • HERE: q = 1 and Φ t =0 = 0 , Π t =0 = −L n Φ = 0 Scalar field evolution – equatorial plane H. Witek (KCL) 9 / 16
Results Scalar radiation measured at r ex / M = 40 0.6 Φ 22 0.4 0.2 r ex Φ 22 0 -0.2 -0.4 0.08 -0.6 Φ 44 0.06 0.04 r ex Φ 44 0.02 0 -0.02 -0.04 -0.06 -0.08 0.08 Ψ 4,22 0.06 0.04 r ex Ψ 4,22 0.02 0 -0.02 -0.04 -0.06 -0.08 0 200 400 600 800 1000 1200 (t - r ex - t junk ) / M • excitation of scalar radiation in l = m = 2 and l = m = 4 sourced by curvature / orbital dynamics • post-merger ringdown H. Witek (KCL) 10 / 16
Results Scalar field waveforms with m = 0, measured at r ex / M = 40 25 Φ 00 20 r ex Φ 00 15 10 5 20 Φ 20 0 -20 -40 ex Φ 20 -60 -80 r 3 -100 -120 -140 0 200 400 600 800 1000 1200 (t - r ex - t junk ) / M • non-trivial scalar excitation • post merger: approach to analytic solution M 3 M P 0 ∼ 2 α GB P 2 ∼ − α GB M 2 χ 2 Φ ∼P 0 r + P 2 r 3 Y 20 M 2 H. Witek (KCL) 11 / 16
Summary and Outlook Take home message: • study black holes in Einstein-dilaton Gauss-Bonnet theory • motivated from “stringy” models • black holes have hair – fundamentally different from GR • first nonlinear study of BH binaries (up to O ( α (1) GB )) → burst of scalar radiation excited in late inspiral & merger → settling down to hairy, rotating solution at late times Outlook • extension to O ( α 2 GB ) within EFT approach → include deformation of metric and GW signal • modelling as full theory? PDE structure within BSSN+puncture gauge approach • construct inspiral-merger-ringdown signal for GW searches Thank you! acknowledgements: H. Witek (KCL) 12 / 16
H. Witek (KCL) 13 / 16
Constraints on EdGB • theoretical constraint: � α GB � � 1 • static BHs only exist for � � √ M 2 2 3 (Kanti et al ’95, Sotiriou & Zhou ’14) • strongest observational constraint: • orbital decay of x-ray binaries ˙ L with ˙ ˙ L ∼ ˙ 5 α 2 GB v − 2 � P L � P ∼ L GR 1 + 96 ¯ � ⇒ | α GB | � 2 km (Yagi ’12) • What can GWs do for us? Not much, actually • due to degeneracies between spin magnitudes, component masses & coupling • modification of GW phase & amplitude not present | α GB | � δ 1 / 4 ( r 12 / m ) − 1 / 4 � in noise ⇒ • with δ ∼ 4%, r 12 = 2 m , m ∼ 30 M ⊙ , χ ∼ 0: � | α GB | � 23 km H. Witek (KCL) 14 / 16
Testing strong field gravity (LSC/LVC ’16, ’17) Consistency tests • consistent parameter estimation from inspiral & inspiral-merger-ringdown • post-peak data consistent with QNM Null tests • substract best GR fit from data: remainder consistent with noise • constraints on parametrized post-Newtonian Modified dispersion relations E 2 = p 2 c 2 + Ap α c α • constraint on graviton Compton wavelength: λ G ≥ 1 . 6 · 10 13 km ( m G � 7 . 7 · 10 − 23 eV / c 2 ) back H. Witek (KCL) 15 / 16
Future prospects – multiband GW astronomy • extreme mass ratio inspirals • multipolar structure • Kerr nature • post-merger of massive binaries • ringdown modes • tests of “no-hair” theorems (LISA consortium ’17) testing for • additional radiation channels • propagation properties • presence of light fundamental fields (Sesana ’16; see also Vitale ’16) H. Witek (KCL) 16 / 16
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