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Vanishing of Nonlinear Tidal Love Numbers of Schwarzschild Black Holes (2312.05065v2)

Published 8 Dec 2023 in gr-qc and hep-th

Abstract: It is well known that asymptotically flat Schwarzschild black holes in general relativity in four spacetime dimensions have vanishing induced linear tidal response. We extend this result beyond linear order for the polar sector, by solving the static nonlinear Einstein equations for the perturbations of the Schwarzschild metric and computing the quadratic corrections to the electric-type tidal Love numbers. After explicitly performing the matching with the point-particle effective theory at leading order in the derivative expansion, we show that the Love number couplings remain zero at higher order in perturbation theory.

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References (63)
  1. L. Baiotti and L. Rezzolla, “Binary neutron star mergers: a review of Einstein’s richest laboratory,” Rept. Prog. Phys. 80 (2017) no. 9, 096901, arXiv:1607.03540 [gr-qc].
  2. L. Hui, A. Joyce, R. Penco, L. Santoni, and A. R. Solomon, “Ladder symmetries of black holes. Implications for love numbers and no-hair theorems,” JCAP 01 (2022) no. 01, 032, arXiv:2105.01069 [hep-th].
  3. L. Hui, A. Joyce, R. Penco, L. Santoni, and A. R. Solomon, “Near-zone symmetries of Kerr black holes,” JHEP 09 (2022) 049, arXiv:2203.08832 [hep-th].
  4. P. Charalambous, S. Dubovsky, and M. M. Ivanov, “Hidden Symmetry of Vanishing Love Numbers,” Phys. Rev. Lett. 127 (2021) no. 10, 101101, arXiv:2103.01234 [hep-th].
  5. M. Perry and M. J. Rodriguez, “Dynamical Love Numbers for Kerr Black Holes,” arXiv:2310.03660 [gr-qc].
  6. H. S. Chia, T. D. P. Edwards, D. Wadekar, A. Zimmerman, S. Olsen, J. Roulet, T. Venumadhav, B. Zackay, and M. Zaldarriaga, “In Pursuit of Love: First Templated Search for Compact Objects with Large Tidal Deformabilities in the LIGO-Virgo Data,” arXiv:2306.00050 [gr-qc].
  7. D. Bini, T. Damour, and A. Geralico, “Novel approach to binary dynamics: application to the fifth post-Newtonian level,” Phys. Rev. Lett. 123 (2019) no. 23, 231104, arXiv:1909.02375 [gr-qc].
  8. C. Dlapa, G. Kälin, Z. Liu, and R. A. Porto, “Conservative Dynamics of Binary Systems at Fourth Post-Minkowskian Order in the Large-Eccentricity Expansion,” Phys. Rev. Lett. 128 (2022) no. 16, 161104, arXiv:2112.11296 [hep-th].
  9. C. Dlapa, G. Kälin, Z. Liu, J. Neef, and R. A. Porto, “Radiation Reaction and Gravitational Waves at Fourth Post-Minkowskian Order,” Phys. Rev. Lett. 130 (2023) no. 10, 101401, arXiv:2210.05541 [hep-th].
  10. Z. Bern, J. Parra-Martinez, R. Roiban, M. S. Ruf, C.-H. Shen, M. P. Solon, and M. Zeng, “Scattering amplitudes and conservative dynamics at the fourth post-Minkowskian order,” PoS LL2022 (2022) 051.
  11. G. U. Jakobsen, G. Mogull, J. Plefka, and B. Sauer, “Dissipative scattering of spinning black holes at fourth post-Minkowskian order,” arXiv:2308.11514 [hep-th].
  12. G. Kälin, Z. Liu, and R. A. Porto, “Conservative Tidal Effects in Compact Binary Systems to Next-to-Leading Post-Minkowskian Order,” Phys. Rev. D 102 (2020) 124025, arXiv:2008.06047 [hep-th].
  13. Q. Henry, G. Faye, and L. Blanchet, “Tidal effects in the gravitational-wave phase evolution of compact binary systems to next-to-next-to-leading post-Newtonian order,” Phys. Rev. D 102 (2020) no. 4, 044033, arXiv:2005.13367 [gr-qc]. [Erratum: Phys.Rev.D 108, 089901 (2023)].
  14. S. Mougiakakos, M. M. Riva, and F. Vernizzi, “Gravitational Bremsstrahlung with Tidal Effects in the Post-Minkowskian Expansion,” Phys. Rev. Lett. 129 (2022) no. 12, 121101, arXiv:2204.06556 [hep-th].
  15. C. Heissenberg, “Angular Momentum Loss due to Tidal Effects in the Post-Minkowskian Expansion,” Phys. Rev. Lett. 131 (2023) no. 1, 011603, arXiv:2210.15689 [hep-th].
  16. G. U. Jakobsen, G. Mogull, J. Plefka, and B. Sauer, “Tidal effects and renormalization at fourth post-Minkowskian order,” arXiv:2312.00719 [hep-th].
  17. T. Damour and A. Nagar, “Relativistic tidal properties of neutron stars,” Phys. Rev. D 80 (2009) 084035, arXiv:0906.0096 [gr-qc].
  18. T. Binnington and E. Poisson, “Relativistic theory of tidal Love numbers,” Phys. Rev. D80 (2009) 084018, arXiv:0906.1366 [gr-qc].
  19. H. Fang and G. Lovelace, “Tidal coupling of a Schwarzschild black hole and circularly orbiting moon,” Phys. Rev. D72 (2005) 124016, arXiv:gr-qc/0505156 [gr-qc].
  20. B. Kol and M. Smolkin, “Black hole stereotyping: Induced gravito-static polarization,” JHEP 02 (2012) 010, arXiv:1110.3764 [hep-th].
  21. S. Chakrabarti, T. Delsate, and J. Steinhoff, “New perspectives on neutron star and black hole spectroscopy and dynamic tides,” arXiv:1304.2228 [gr-qc].
  22. N. Gürlebeck, “No-hair theorem for Black Holes in Astrophysical Environments,” Phys. Rev. Lett. 114 (2015) no. 15, 151102, arXiv:1503.03240 [gr-qc].
  23. R. A. Porto, “The Tune of Love and the Nature(ness) of Spacetime,” Fortsch. Phys. 64 (2016) no. 10, 723–729, arXiv:1606.08895 [gr-qc].
  24. A. Le Tiec and M. Casals, “Spinning Black Holes Fall in Love,” Phys. Rev. Lett. 126 (2021) no. 13, 131102, arXiv:2007.00214 [gr-qc].
  25. A. Le Tiec, M. Casals, and E. Franzin, “Tidal Love Numbers of Kerr Black Holes,” Phys. Rev. D 103 (2021) no. 8, 084021, arXiv:2010.15795 [gr-qc].
  26. H. S. Chia, “Tidal deformation and dissipation of rotating black holes,” Phys. Rev. D 104 (2021) no. 2, 024013, arXiv:2010.07300 [gr-qc].
  27. P. Charalambous, S. Dubovsky, and M. M. Ivanov, “On the Vanishing of Love Numbers for Kerr Black Holes,” JHEP 05 (2021) 038, arXiv:2102.08917 [hep-th].
  28. L. Hui, A. Joyce, R. Penco, L. Santoni, and A. R. Solomon, “Static response and Love numbers of Schwarzschild black holes,” JCAP 04 (2021) 052, arXiv:2010.00593 [hep-th].
  29. D. Pereñiguez and V. Cardoso, “Love numbers and magnetic susceptibility of charged black holes,” Phys. Rev. D 105 (2022) no. 4, 044026, arXiv:2112.08400 [gr-qc].
  30. M. J. Rodriguez, L. Santoni, A. R. Solomon, and L. F. Temoche, “Love numbers for rotating black holes in higher dimensions,” Phys. Rev. D 108 (2023) no. 8, 084011, arXiv:2304.03743 [hep-th].
  31. P. Charalambous and M. M. Ivanov, “Scalar Love numbers and Love symmetries of 5-dimensional Myers-Perry black holes,” JHEP 07 (2023) 222, arXiv:2303.16036 [hep-th].
  32. K. Ioka and H. Nakano, “Second and higher-order quasi-normal modes in binary black hole mergers,” Phys. Rev. D 76 (2007) 061503, arXiv:0704.3467 [astro-ph].
  33. H. Nakano and K. Ioka, “Second Order Quasi-Normal Mode of the Schwarzschild Black Hole,” Phys. Rev. D 76 (2007) 084007, arXiv:0708.0450 [gr-qc].
  34. M. Lagos and L. Hui, “Generation and propagation of nonlinear quasinormal modes of a Schwarzschild black hole,” Phys. Rev. D 107 (2023) no. 4, 044040, arXiv:2208.07379 [gr-qc].
  35. A. Kehagias, D. Perrone, A. Riotto, and F. Riva, “Explaining nonlinearities in black hole ringdowns from symmetries,” Phys. Rev. D 108 (2023) no. 2, L021501, arXiv:2301.09345 [gr-qc].
  36. D. Perrone, T. Barreira, A. Kehagias, and A. Riotto, “Non-linear Black Hole Ringdowns: an Analytical Approach,” arXiv:2308.15886 [gr-qc].
  37. B. Bucciotti, A. Kuntz, F. Serra, and E. Trincherini, “Nonlinear Quasi-Normal Modes: Uniform Approximation,” arXiv:2309.08501 [hep-th].
  38. E. Poisson, “Compact body in a tidal environment: New types of relativistic Love numbers, and a post-Newtonian operational definition for tidally induced multipole moments,” Phys. Rev. D 103 (2021) no. 6, 064023, arXiv:2012.10184 [gr-qc].
  39. E. Poisson, “Tidally induced multipole moments of a nonrotating black hole vanish to all post-Newtonian orders,” Phys. Rev. D 104 (2021) no. 10, 104062, arXiv:2108.07328 [gr-qc].
  40. V. De Luca, J. Khoury, and S. S. C. Wong, “Nonlinearities in the tidal Love numbers of black holes,” Phys. Rev. D 108 (2023) no. 2, 024048, arXiv:2305.14444 [gr-qc].
  41. W. D. Goldberger and I. Z. Rothstein, “An Effective field theory of gravity for extended objects,” Phys. Rev. D 73 (2006) 104029, arXiv:hep-th/0409156.
  42. W. D. Goldberger, “Les Houches lectures on effective field theories and gravitational radiation,” in Les Houches Summer School - Session 86: Particle Physics and Cosmology: The Fabric of Spacetime. 1, 2007. arXiv:hep-ph/0701129.
  43. R. A. Porto, “The effective field theorist’s approach to gravitational dynamics,” Phys. Rept. 633 (2016) 1–104, arXiv:1601.04914 [hep-th].
  44. W. D. Goldberger and I. Z. Rothstein, “Dissipative effects in the worldline approach to black hole dynamics,” Phys. Rev. D 73 (2006) 104030, arXiv:hep-th/0511133.
  45. W. D. Goldberger, J. Li, and I. Z. Rothstein, “Non-conservative effects on spinning black holes from world-line effective field theory,” JHEP 06 (2021) 053, arXiv:2012.14869 [hep-th].
  46. D. Bini, T. Damour, and A. Geralico, “Scattering of tidally interacting bodies in post-Minkowskian gravity,” Phys. Rev. D 101 (2020) no. 4, 044039, arXiv:2001.00352 [gr-qc].
  47. K. Haddad and A. Helset, “Tidal effects in quantum field theory,” JHEP 12 (2020) 024, arXiv:2008.04920 [hep-th].
  48. Z. Bern, J. Parra-Martinez, R. Roiban, E. Sawyer, and C.-H. Shen, “Leading Nonlinear Tidal Effects and Scattering Amplitudes,” JHEP 05 (2021) 188, arXiv:2010.08559 [hep-th].
  49. T. Regge and J. A. Wheeler, “Stability of a Schwarzschild singularity,” Phys. Rev. 108 (1957) 1063–1069.
  50. B. S. DeWitt, “Quantum Theory of Gravity. 2. The Manifestly Covariant Theory,” Phys. Rev. 162 (1967) 1195–1239.
  51. G. ’t Hooft and M. J. G. Veltman, “One loop divergencies in the theory of gravitation,” Ann. Inst. H. Poincare Phys. Theor. A 20 (1974) 69–94.
  52. L. F. Abbott, “The Background Field Method Beyond One Loop,” Nucl. Phys. B 185 (1981) 189–203.
  53. M. J. Duff, “Quantum Tree Graphs and the Schwarzschild Solution,” Phys. Rev. D 7 (1973) 2317–2326.
  54. M. M. Ivanov and Z. Zhou, “Revisiting the matching of black hole tidal responses: A systematic study of relativistic and logarithmic corrections,” Phys. Rev. D 107 (2023) no. 8, 084030, arXiv:2208.08459 [hep-th].
  55. M. M. Riva, L. Santoni, N. Savić, and F. Vernizzi, “in preparation,”.
  56. P. Charalambous, S. Dubovsky, and M. M. Ivanov, “Love symmetry,” JHEP 10 (2022) 175, arXiv:2209.02091 [hep-th].
  57. R. A. Rosen and L. Santoni, “Black hole perturbations of massive and partially massless spin-2 fields in (anti) de Sitter spacetime,” JHEP 03 (2021) 139, arXiv:2010.00595 [hep-th].
  58. G. Franciolini, L. Hui, R. Penco, L. Santoni, and E. Trincherini, “Effective Field Theory of Black Hole Quasinormal Modes in Scalar-Tensor Theories,” JHEP 02 (2019) 127, arXiv:1810.07706 [hep-th].
  59. D. Brizuela, J. M. Martin-Garcia, and M. Tiglio, “A Complete gauge-invariant formalism for arbitrary second-order perturbations of a Schwarzschild black hole,” Phys. Rev. D 80 (2009) 024021, arXiv:0903.1134 [gr-qc].
  60. H. Motohashi, T. Suyama, and K. Takahashi, “Fundamental theorem on gauge fixing at the action level,” Phys. Rev. D 94 (2016) no. 12, 124021, arXiv:1608.00071 [gr-qc].
  61. T. Hinderer, “Tidal Love numbers of neutron stars,” Astrophys. J. 677 (2008) 1216–1220, arXiv:0711.2420 [astro-ph].
  62. H. Bateman and A. Erdélyi, Higher transcendental functions. Calif. Inst. Technol. Bateman Manuscr. Project. McGraw-Hill, New York, NY, 1955. https://cds.cern.ch/record/100233.
  63. J. M. Martín-García, “xAct: Efficient tensor computer algebra for the Wolfram Language.”. http://www.xact.es/.
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