Abstract
Using Effective Field Theory (EFT) methods, we compute the effects of horizon dissipation on the gravitational interactions of relativistic binary black hole systems. We assume that the dynamics is perturbative, i.e it admits an expansion in powers of Newton’s constant (post-Minkowskian, or PM, approximation). As applications, we compute corrections to the scattering angle in a black hole collision due to dissipative effects to leading PM order, as well as the post-Newtonian (PN) corrections to the equations of motion of binary black holes in non-relativistic orbits, which represents the leading order finite size effect in the equations of motion. The methods developed here are also applicable to the case of more general compact objects, eg. neutron stars, where the magnitude of the dissipative effects depends on non-gravitational physics (e.g, the equation of state for nuclear matter).
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
LIGO Scientific, Virgo collaboration, Observation of gravitational waves from a binary black hole merger, Phys. Rev. Lett. 116 (2016) 061102 [arXiv:1602.03837] [INSPIRE].
LIGO Scientific, Virgo collaboration, GW170817: observation of gravitational waves from a binary neutron star inspiral, Phys. Rev. Lett. 119 (2017) 161101 [arXiv:1710.05832] [INSPIRE].
T. Binnington and E. Poisson, Relativistic theory of tidal Love numbers, Phys. Rev. D 80 (2009) 084018 [arXiv:0906.1366] [INSPIRE].
T. Damour and O.M. Lecian, On the gravitational polarizability of black holes, Phys. Rev. D 80 (2009) 044017 [arXiv:0906.3003] [INSPIRE].
B. Kol and M. Smolkin, Black hole stereotyping: induced gravito-static polarization, JHEP 02 (2012) 010 [arXiv:1110.3764] [INSPIRE].
E.E. Flanagan and T. Hinderer, Constraining neutron star tidal Love numbers with gravitational wave detectors, Phys. Rev. D 77 (2008) 021502 [arXiv:0709.1915] [INSPIRE].
T. Hinderer, Tidal Love numbers of neutron stars, Astrophys. J. 677 (2008) 1216 [arXiv:0711.2420] [INSPIRE].
E. Poisson and M. Sasaki, Gravitational radiation from a particle in circular orbit around a black hole. 5: black hole absorption and tail corrections, Phys. Rev. D 51 (1995) 5753 [gr-qc/9412027] [INSPIRE].
H. Tagoshi, S. Mano and E. Takasugi, PostNewtonian expansion of gravitational waves from a particle in circular orbits around a rotating black hole: effects of black hole absorption, Prog. Theor. Phys. 98 (1997) 829 [gr-qc/9711072] [INSPIRE].
E. Poisson, Absorption of mass and angular momentum by a black hole: time-domain formalisms for gravitational perturbations, and the small-hole/slow-motion approximation, Phys. Rev. D 70 (2004) 084044 [gr-qc/0407050] [INSPIRE].
W.D. Goldberger and I.Z. Rothstein, Dissipative effects in the worldline approach to black hole dynamics, Phys. Rev. D 73 (2006) 104030 [hep-th/0511133] [INSPIRE].
W.D. Goldberger and I.Z. Rothstein, An effective field theory of gravity for extended objects, Phys. Rev. D 73 (2006) 104029 [hep-th/0409156] [INSPIRE].
W.D. Goldberger and I.Z. Rothstein, Towers of Gravitational Theories, Int. J. Mod. Phys. D 15 (2006) 2293 [Gen. Rel. Grav. 38 (2006) 1537] [hep-th/0605238]. [INSPIRE].
R.A. Porto, Absorption effects due to spin in the worldline approach to black hole dynamics, Phys. Rev. D 77 (2008) 064026 [arXiv:0710.5150] [INSPIRE].
W.D. Goldberger and I.Z. Rothstein, An effective field theory of quantum mechanical black hole horizons, JHEP 04 (2020) 056 [arXiv:1912.13435] [INSPIRE].
C.R. Galley and M. Tiglio, Radiation reaction and gravitational waves in the effective field theory approach, Phys. Rev. D 79 (2009) 124027 [arXiv:0903.1122] [INSPIRE].
J.S. Schwinger, Brownian motion of a quantum oscillator, J. Math. Phys. 2 (1961) 407 [INSPIRE].
L.V. Keldysh, Diagram technique for nonequilibrium processes, Zh. Eksp. Teor. Fiz. 47 (1964) 1515 [Sov. Phys. JETP 20 (1965) 1018] [INSPIRE].
W.L. Burke and K.S. Thorne, Gravitational radiation damping, in Relativity, M. Carmeli et al. eds., Plenum Press, New York U.S.A. (1970).
S. Endlich and R. Penco, Effective field theory approach to tidal dynamics of spinning astrophysical systems, Phys. Rev. D 93 (2016) 064021 [arXiv:1510.08889] [INSPIRE].
W.D. Goldberger and I.Z. Rothstein, Virtual Hawking radiation, arXiv:2007.00726 [INSPIRE].
K. Westpfahl and M. Goller, Gravitational scattering of two relativistic particles in postlinear approximation, Lett. Nuovo Cim. 26 (1979) 573 [INSPIRE].
M. Portilla, Scattering of two gravitating particles: classical approach, J. Phys. A 13 (1980) 3677 [INSPIRE].
L. Bel, T. Damour, N. Deruelle, J. Ibáñez and J. Martin, Poincaré-invariant gravitational field and equations of motion of two pointlike objects: The postlinear approximation of general relativity, Gen. Rel. Grav. 13 (1981) 963 [INSPIRE].
T. Damour, Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory, Phys. Rev. D 94 (2016) 104015 [arXiv:1609.00354] [INSPIRE].
J. Vines, Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings, Class. Quant. Grav. 35 (2018) 084002 [arXiv:1709.06016] [INSPIRE].
T. Damour, High-energy gravitational scattering and the general relativistic two-body problem, Phys. Rev. D 97 (2018) 044038 [arXiv:1710.10599] [INSPIRE].
D. Bini and T. Damour, Gravitational spin-orbit coupling in binary systems at the second post-Minkowskian approximation, Phys. Rev. D 98 (2018) 044036 [arXiv:1805.10809] [INSPIRE].
J. Vines, J. Steinhoff and A. Buonanno, Spinning-black-hole scattering and the test-black-hole limit at second post-Minkowskian order, Phys. Rev. D 99 (2019) 064054 [arXiv:1812.00956] [INSPIRE].
A. Antonelli, A. Buonanno, J. Steinhoff, M. van de Meent and J. Vines, Energetics of two-body Hamiltonians in post-Minkowskian gravity, Phys. Rev. D 99 (2019) 104004 [arXiv:1901.07102] [INSPIRE].
N. Siemonsen and J. Vines, Test black holes, scattering amplitudes and perturbations of Kerr spacetime, Phys. Rev. D 101 (2020) 064066 [arXiv:1909.07361] [INSPIRE].
G. Kälin and R.A. Porto, From boundary data to bound states, JHEP 01 (2020) 072 [arXiv:1910.03008] [INSPIRE].
G. Kälin and R.A. Porto, From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist), JHEP 02 (2020) 120 [arXiv:1911.09130] [INSPIRE].
T. Damour, Classical and quantum scattering in post-Minkowskian gravity, Phys. Rev. D 102 (2020) 024060 [arXiv:1912.02139] [INSPIRE].
D. Bini, T. Damour and A. Geralico, Scattering of tidally interacting bodies in post-Minkowskian gravity, Phys. Rev. D 101 (2020) 044039 [arXiv:2001.00352] [INSPIRE].
A. Buonanno and T. Damour, Effective one-body approach to general relativistic two-body dynamics, Phys. Rev. D 59 (1999) 084006 [gr-qc/9811091] [INSPIRE].
A. Buonanno and T. Damour, Transition from inspiral to plunge in binary black hole coalescences, Phys. Rev. D 62 (2000) 064015 [gr-qc/0001013] [INSPIRE].
D. Neill and I.Z. Rothstein, Classical space-times from the S matrix, Nucl. Phys. B 877 (2013) 177 [arXiv:1304.7263] [INSPIRE].
F. Cachazo and A. Guevara, Leading singularities and classical gravitational scattering, JHEP 02 (2020) 181 [arXiv:1705.10262] [INSPIRE].
C. Cheung, I.Z. Rothstein and M.P. Solon, From scattering amplitudes to classical potentials in the post-Minkowskian expansion, Phys. Rev. Lett. 121 (2018) 251101 [arXiv:1808.02489] [INSPIRE].
D.A. Kosower, B. Maybee and D. O’Connell, Amplitudes, observables, and classical scattering, JHEP 02 (2019) 137 [arXiv:1811.10950] [INSPIRE].
A. Guevara, A. Ochirov and J. Vines, Scattering of spinning black holes from exponentiated soft factors, JHEP 09 (2019) 056 [arXiv:1812.06895] [INSPIRE].
Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M.P. Solon and M. Zeng, Scattering amplitudes and the conservative Hamiltonian for binary systems at third post-Minkowskian order, Phys. Rev. Lett. 122 (2019) 201603 [arXiv:1901.04424] [INSPIRE].
Y.F. Bautista and A. Guevara, From scattering amplitudes to classical physics: universality, double copy and soft theorems, arXiv:1903.12419 [INSPIRE].
A. Cristofoli, N.E.J. Bjerrum-Bohr, P.H. Damgaard and P. Vanhove, Post-Minkowskian Hamiltonians in general relativity, Phys. Rev. D 100 (2019) 084040 [arXiv:1906.01579] [INSPIRE].
B. Maybee, D. O’Connell and J. Vines, Observables and amplitudes for spinning particles and black holes, JHEP 12 (2019) 156 [arXiv:1906.09260] [INSPIRE].
A. Guevara, A. Ochirov and J. Vines, Black-hole scattering with general spin directions from minimal-coupling amplitudes, Phys. Rev. D 100 (2019) 104024 [arXiv:1906.10071] [INSPIRE].
Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M.P. Solon and M. Zeng, Black hole binary dynamics from the double copy and effective theory, JHEP 10 (2019) 206 [arXiv:1908.01493] [INSPIRE].
N.E.J. Bjerrum-Bohr, A. Cristofoli and P.H. Damgaard, Post-Minkowskian scattering angle in Einstein gravity, JHEP 08 (2020) 038 [arXiv:1910.09366] [INSPIRE].
A. Cristofoli, P.H. Damgaard, P. Di Vecchia and C. Heissenberg, Second-order post-Minkowskian scattering in arbitrary dimensions, JHEP 07 (2020) 122 [arXiv:2003.10274] [INSPIRE].
C. Cheung and M.P. Solon, Tidal effects in the post-Minkowskian expansion, arXiv:2006.06665 [INSPIRE].
W.D. Goldberger and I.Z. Rothstein, unpublished.
I.Z. Rothstein, Progress in effective field theory approach to the binary inspiral problem, Gen. Rel. Grav. 46 (2014) 1726 [INSPIRE].
R. Mertig, M. Böhm and A. Denner, FEYN CALC: computer algebraic calculation of Feynman amplitudes, Comput. Phys. Commun. 64 (1991) 345 [INSPIRE].
V. Shtabovenko, R. Mertig and F. Orellana, New developments in FeynCalc 9.0, Comput. Phys. Commun. 207 (2016) 432 [arXiv:1601.01167] [INSPIRE].
S.W. Hawking, Black holes in general relativity, Commun. Math. Phys. 25 (1972) 152 [INSPIRE].
A.A. Starobinskii and S.M. Churilov, Amplification of electromagnetic and gravitational waves scattered by a rotating “black hole”, Zh. Eksp. Teor. Fiz. 65 (1973) 3.
S. Endlich and R. Penco, A modern approach to superradiance, JHEP 05 (2017) 052 [arXiv:1609.06723] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2007.00731
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Goldberger, W.D., Rothstein, I.Z. Horizon radiation reaction forces. J. High Energ. Phys. 2020, 26 (2020). https://doi.org/10.1007/JHEP10(2020)026
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2020)026