Abstract
We generalize the worldline EFT formalism developed in [4–9] to calculate the non-conservative tidal effects on spinning black holes in a long wavelength approximation that is valid to all orders in the magnitude of the spin. We present results for the rate of change of mass and angular momentum in a background field and find agreement with previous calculations obtained by different techniques. We also present new results for both the non-conservative equations of motion and power loss/gain for a binary inspiral, which start at 5PN and 2.5PN order respectively and manifest the Penrose process.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
K.S. Thorne and J.B. Hartle, Laws of motion and precession for black holes and other bodies, Phys. Rev. D 31 (1984) 1815 [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].
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, Gen. Rel. Grav. 38 (2006) 1537 [Int. J. Mod. Phys. D 15 (2006) 2293] [hep-th/0605238] [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 Quantum Mechanical Black Hole Horizons, JHEP 04 (2020) 056 [arXiv:1912.13435] [INSPIRE].
W.D. Goldberger and I.Z. Rothstein, Horizon radiation reaction forces, JHEP 10 (2020) 026 [arXiv:2007.00731] [INSPIRE].
W.D. Goldberger and I.Z. Rothstein, Virtual Hawking Radiation, Phys. Rev. Lett. 125 (2020) 211301 [arXiv:2007.00726] [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].
R.A. Porto and I.Z. Rothstein, The hyperfine Einstein-Infeld-Hoffmann potential, Phys. Rev. Lett. 97 (2006) 021101 [gr-qc/0604099] [INSPIRE].
S. Endlich and R. Penco, A Modern Approach to Superradiance, JHEP 05 (2017) 052 [arXiv:1609.06723] [INSPIRE].
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].
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].
R.A. Porto, Post-Newtonian corrections to the motion of spinning bodies in NRGR, Phys. Rev. D 73 (2006) 104031 [gr-qc/0511061] [INSPIRE].
A.J. Hanson and T. Regge, The Relativistic Spherical Top, Annals Phys. 87 (1974) 498 [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.
D.N. Page, Particle Emission Rates from a Black Hole: Massless Particles from an Uncharged, Nonrotating Hole, Phys. Rev. D 13 (1976) 198 [INSPIRE].
H.S. Chia, Tidal Deformation and Dissipation of Rotating Black Holes, arXiv:2010.07300 [INSPIRE].
P.D. D’Eath, Dynamics of a small black hole in a background universe, Phys. Rev. D 11 (1975) 1387 [INSPIRE].
K. Alvi, Energy and angular momentum flow into a black hole in a binary, Phys. Rev. D 64 (2001) 104020 [gr-qc/0107080] [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].
K. Chatziioannou, E. Poisson and N. Yunes, Tidal heating and torquing of a Kerr black hole to next-to-leading order in the tidal coupling, Phys. Rev. D 87 (2013) 044022 [arXiv:1211.1686] [INSPIRE].
K. Chatziioannou, E. Poisson and N. Yunes, Improved next-to-leading order tidal heating and torquing of a Kerr black hole, Phys. Rev. D 94 (2016) 084043 [arXiv:1608.02899] [INSPIRE].
M.H.L. Pryce, Commuting co-ordinates in the new field theory, Proc. Roy. Soc. Lond. A 150 (1935) 166 [INSPIRE].
M. Henneaux and C. Teitelboim, Quantization of gauge systems, Princeton University Press (1992).
M. Mathisson, Neue mechanik materieller systemes, Acta Phys. Polon. 163 (1937).
W.G. Dixon, Dynamics of extended bodies in general relativity. I. Momentum and angular momentum, Proc. Roy. Soc. Lond. A 314 (1970) 499 [INSPIRE].
A. Papapetrou, Spinning test particles in general relativity. 1., Proc. Roy. Soc. Lond. A 209 (1951) 248 [INSPIRE].
S.W. Hawking, Perturbations of an expanding universe, Astrophys. J. 145 (1966) 544 [INSPIRE].
D.G. Boulware, Quantum Field Theory in Schwarzschild and Rindler Spaces, Phys. Rev. D 11 (1975) 1404 [INSPIRE].
W.G. Unruh, Notes on black hole evaporation, Phys. Rev. D 14 (1976) 870 [INSPIRE].
R.O. Hansen, Multipole moments of stationary space-times, J. Math. Phys. 15 (1974) 46 [INSPIRE].
A. Le Tiec and M. Casals, Spinning Black Holes Fall in Love, Phys. Rev. Lett. 126 (2021) 131102 [arXiv:2007.00214] [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].
P. Pani, L. Gualtieri, A. Maselli and V. Ferrari, Tidal deformations of a spinning compact object, Phys. Rev. D 92 (2015) 024010 [arXiv:1503.07365] [INSPIRE].
S.W. Hawking, Black holes in general relativity, Commun. Math. Phys. 25 (1972) 152 [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].
W.D. Goldberger, talk given at the workshop Rethinking the Relativistic Two-body Problem, Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Aug. 24–28, 2020, https://workshops.aei.mpg.de/gwuniverse/.
A. Le Tiec, M. Casals and E. Franzin, Tidal Love Numbers of Kerr Black Holes, Phys. Rev. D 103 (2021) 084021 [arXiv:2010.15795] [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: 2012.14869
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., Li, J. & Rothstein, I.Z. Non-conservative effects on spinning black holes from world-line effective field theory. J. High Energ. Phys. 2021, 53 (2021). https://doi.org/10.1007/JHEP06(2021)053
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2021)053