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Ladder Symmetries and Love Numbers of Reissner--Nordström Black Holes (2404.06544v2)

Published 9 Apr 2024 in gr-qc and hep-th

Abstract: It is well known that asymptotically flat black holes in general relativity have vanishing tidal Love numbers. In the case of Schwarzschild and Kerr black holes, this property has been shown to be a consequence of a hidden structure of ladder symmetries for the perturbations. In this work, we extend the ladder symmetries to non-rotating charged black holes in general relativity. As opposed to previous works in this context, we adopt a more general definition of Love numbers, including quadratic operators that mix gravitational and electromagnetic perturbations in the point-particle effective field theory. We show that the calculation of a subset of those couplings in full general relativity is affected by an ambiguity in the split between source and response, which we resolve through an analytic continuation. As a result, we derive a novel master equation that unifies scalar, electromagnetic and gravitational perturbations around Reissner--Nordstr\"om black holes. The equation is hypergeometric and can be obtained from previous formulations via nontrivial field redefinitions, which allow to systematically remove some of the singularities and make the presence of the ladder symmetries more manifest.

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References (83)
  1. E. Berti, V. Cardoso, Z. Haiman, D. E. Holz, E. Mottola, S. Mukherjee, B. Sathyaprakash, X. Siemens, and N. Yunes, “Snowmass2021 Cosmic Frontier White Paper: Fundamental Physics and Beyond the Standard Model,” in Snowmass 2021. 3, 2022. arXiv:2203.06240 [hep-ph].
  2. A. Buonanno, M. Khalil, D. O’Connell, R. Roiban, M. P. Solon, and M. Zeng, “Snowmass White Paper: Gravitational Waves and Scattering Amplitudes,” in Snowmass 2021. 4, 2022. arXiv:2204.05194 [hep-th].
  3. 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 [astro-ph].
  4. J. Vines, E. E. Flanagan, and T. Hinderer, “Post-1-Newtonian tidal effects in the gravitational waveform from binary inspirals,” Phys. Rev. D 83 (2011) 084051, arXiv:1101.1673 [gr-qc].
  5. D. Bini, T. Damour, and G. Faye, “Effective action approach to higher-order relativistic tidal interactions in binary systems and their effective one body description,” Phys. Rev. D 85 (2012) 124034, arXiv:1202.3565 [gr-qc].
  6. A. W. Steiner, S. Gandolfi, F. J. Fattoyev, and W. G. Newton, “Using Neutron Star Observations to Determine Crust Thicknesses, Moments of Inertia, and Tidal Deformabilities,” Phys. Rev. C 91 (2015) no. 1, 015804, arXiv:1403.7546 [nucl-th].
  7. J. M. Lattimer and M. Prakash, “The Equation of State of Hot, Dense Matter and Neutron Stars,” Phys. Rept. 621 (2016) 127–164, arXiv:1512.07820 [astro-ph.SR].
  8. F. Iacovelli, M. Mancarella, C. Mondal, A. Puecher, T. Dietrich, F. Gulminelli, M. Maggiore, and M. Oertel, “Nuclear physics constraints from binary neutron star mergers in the Einstein Telescope era,” Phys. Rev. D 108 (2023) no. 12, 122006, arXiv:2308.12378 [gr-qc].
  9. V. Cardoso, E. Franzin, A. Maselli, P. Pani, and G. Raposo, “Testing strong-field gravity with tidal Love numbers,” Phys. Rev. D 95 (2017) no. 8, 084014, arXiv:1701.01116 [gr-qc]. [Addendum: Phys.Rev.D 95, 089901 (2017)].
  10. E. Franzin, V. Cardoso, P. Pani, and G. Raposo, “Testing strong gravity with gravitational waves and Love numbers,” J. Phys. Conf. Ser. 841 (2017) no. 1, 012035.
  11. V. Cardoso and P. Pani, “Testing the nature of dark compact objects: a status report,” Living Rev. Rel. 22 (2019) no. 1, 4, arXiv:1904.05363 [gr-qc].
  12. P. Pani and A. Maselli, “Love in Extrema Ratio,” Int. J. Mod. Phys. D 28 (2019) no. 14, 1944001, arXiv:1905.03947 [gr-qc].
  13. C. Chirenti, C. Posada, and V. Guedes, “Where is Love? Tidal deformability in the black hole compactness limit,” Class. Quant. Grav. 37 (2020) no. 19, 195017, arXiv:2005.10794 [gr-qc].
  14. 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].
  15. A. E. H. Love, “The yielding of the earth to disturbing forces,” Monthly Notices of the Royal Astronomical Society 69 (1909) 476.
  16. Springer International Publishing, 2016.
  17. H. Fang and G. Lovelace, “Tidal coupling of a Schwarzschild black hole and circularly orbiting moon,” Phys. Rev. D 72 (2005) 124016, arXiv:gr-qc/0505156.
  18. T. Damour and A. Nagar, “Relativistic tidal properties of neutron stars,” Phys. Rev. D 80 (2009) 084035, arXiv:0906.0096 [gr-qc].
  19. T. Binnington and E. Poisson, “Relativistic theory of tidal Love numbers,” Phys. Rev. D 80 (2009) 084018, arXiv:0906.1366 [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. N. Gürlebeck, “No-hair theorem for Black Holes in Astrophysical Environments,” Phys. Rev. Lett. 114 (2015) no. 15, 151102, arXiv:1503.03240 [gr-qc].
  22. 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].
  23. M. M. Ivanov and Z. Zhou, “Vanishing of Black Hole Tidal Love Numbers from Scattering Amplitudes,” Phys. Rev. Lett. 130 (2023) no. 9, 091403, arXiv:2209.14324 [hep-th].
  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. 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].
  29. 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.
  30. 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.
  31. W. D. Goldberger and A. Ross, “Gravitational radiative corrections from effective field theory,” Phys. Rev. D 81 (2010) 124015, arXiv:0912.4254 [gr-qc].
  32. I. Z. Rothstein, “Progress in effective field theory approach to the binary inspiral problem,” Gen. Rel. Grav. 46 (2014) 1726.
  33. R. A. Porto, “The effective field theorist’s approach to gravitational dynamics,” Phys. Rept. 633 (2016) 1–104, arXiv:1601.04914 [hep-th].
  34. M. Levi, “Effective Field Theories of Post-Newtonian Gravity: A comprehensive review,” Rept. Prog. Phys. 83 (2020) no. 7, 075901, arXiv:1807.01699 [hep-th].
  35. 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].
  36. W. D. Goldberger, “Effective field theories of gravity and compact binary dynamics: A Snowmass 2021 whitepaper,” in Snowmass 2021. 6, 2022. arXiv:2206.14249 [hep-th].
  37. W. D. Goldberger, “Effective Field Theory for Compact Binary Dynamics,” arXiv:2212.06677 [hep-th].
  38. 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].
  39. M. M. Riva, L. Santoni, N. Savić, and F. Vernizzi, “Vanishing of Nonlinear Tidal Love Numbers of Schwarzschild Black Holes,” arXiv:2312.05065 [gr-qc].
  40. 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].
  41. 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].
  42. 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].
  43. J. Ben Achour, E. R. Livine, S. Mukohyama, and J.-P. Uzan, “Hidden symmetry of the static response of black holes: applications to Love numbers,” JHEP 07 (2022) 112, arXiv:2202.12828 [gr-qc].
  44. 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].
  45. P. Charalambous, S. Dubovsky, and M. M. Ivanov, “Love symmetry,” JHEP 10 (2022) 175, arXiv:2209.02091 [hep-th].
  46. R. Berens, L. Hui, and Z. Sun, “Ladder symmetries of black holes and de Sitter space: love numbers and quasinormal modes,” JCAP 06 (2023) 056, arXiv:2212.09367 [hep-th].
  47. S. Chandrasekhar, The Mathematical Theory of Black Holes. Clarendon Press, 1998.
  48. F. J. Zerilli, “Perturbation analysis for gravitational and electromagnetic radiation in a reissner-nordstroem geometry,” Phys. Rev. D 9 (1974) 860–868.
  49. V. Moncrief, “Odd-parity stability of a Reissner-Nordstrom black hole,” Phys. Rev. D 9 (1974) 2707–2709.
  50. V. Moncrief, “Stability of Reissner-Nordstrom black holes,” Phys. Rev. D 10 (1974) 1057–1059.
  51. V. Moncrief, “Gauge-invariant perturbations of Reissner-Nordstrom black holes,” Phys. Rev. D 12 (1975) 1526–1537.
  52. S. Slavjanov and L. Wolfgang, Special Functions: A Unified Theory Based on Singularities. Oxford Science Publications. Oxford University Press, 2000.
  53. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1995. With contributions by F. M. Arscott, S. Yu. Slavyanov, D. Schmidt, G. Wolf, P. Maroni and A. Duval.
  54. G. Bonelli, C. Iossa, D. P. Lichtig, and A. Tanzini, “Exact solution of Kerr black hole perturbations via CFT2 and instanton counting: Greybody factor, quasinormal modes, and Love numbers,” Phys. Rev. D 105 (2022) no. 4, 044047, arXiv:2105.04483 [hep-th].
  55. G. Bonelli, C. Iossa, D. Panea Lichtig, and A. Tanzini, “Irregular Liouville Correlators and Connection Formulae for Heun Functions,” Commun. Math. Phys. 397 (2023) no. 2, 635–727, arXiv:2201.04491 [hep-th].
  56. O. Lisovyy and A. Naidiuk, “Perturbative connection formulas for Heun equations,” J. Phys. A 55 (2022) no. 43, 434005, arXiv:2208.01604 [math-ph].
  57. S. Slavyanov and W. Lay, Special Functions: A Unified Theory Based on Singularities. Oxford Science Publications. Oxford University Press, 2000. https://books.google.fr/books?id=JvGCsnd5OMUC.
  58. F. J. Zerilli, “Effective potential for even parity Regge-Wheeler gravitational perturbation equations,” Phys. Rev. Lett. 24 (1970) 737–738.
  59. J. R. Ipser, “Gravitational Radiation from Slowly Rotating, Fully Relativistic Stars,” Astrophysical Journal 166 (1971) 175.
  60. E. D. Fackerell, “Solutions of Zerilli’s Equation for Even-Parity Gravitational Perturbations,” The Astrophysical Journall 166 (1971) 197.
  61. S. Chandrasekhar and S. Detweiler, “The quasi-normal modes of the schwarzschild black hole,” Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 344 (1975) no. 1639, 441–452. http://www.jstor.org/stable/78902.
  62. T. Regge and J. A. Wheeler, “Stability of a Schwarzschild singularity,” Phys. Rev. 108 (1957) 1063–1069.
  63. K. Glampedakis, A. D. Johnson, and D. Kennefick, “Darboux transformation in black hole perturbation theory,” Phys. Rev. D 96 (2017) no. 2, 024036, arXiv:1702.06459 [gr-qc].
  64. McGRAW-HILL book company, 1953.
  65. 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.
  66. P. Pani, E. Berti, and L. Gualtieri, “Gravitoelectromagnetic Perturbations of Kerr-Newman Black Holes: Stability and Isospectrality in the Slow-Rotation Limit,” Phys. Rev. Lett. 110 (2013) no. 24, 241103, arXiv:1304.1160 [gr-qc].
  67. A. R. Solomon, “Off-Shell Duality Invariance of Schwarzschild Perturbation Theory,” Particles 6 (2023) no. 4, 943–974, arXiv:2310.04502 [gr-qc].
  68. S. Chandrasekhar, “On the equations governing the perturbations of the Schwarzschild black hole,” Proc. Roy. Soc. Lond. A 343 (1975) no. 1634, 289–298.
  69. S. Chandrasekhar and S. L. Detweiler, “The quasi-normal modes of the Schwarzschild black hole,” Proc. Roy. Soc. Lond. A 344 (1975) 441–452.
  70. E. Berti, V. Cardoso, and A. O. Starinets, “Quasinormal modes of black holes and black branes,” Class. Quant. Grav. 26 (2009) 163001, arXiv:0905.2975 [gr-qc].
  71. R. Brito, V. Cardoso, and P. Pani, “Partially massless gravitons do not destroy general relativity black holes,” Phys. Rev. D 87 (2013) no. 12, 124024, arXiv:1306.0908 [gr-qc].
  72. 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].
  73. G. W. Gibbons, “Vacuum Polarization and the Spontaneous Loss of Charge by Black Holes,” Commun. Math. Phys. 44 (1975) 245–264.
  74. P. Charalambous, “Love numbers and Love symmetries for p𝑝pitalic_p-form and gravitational perturbations of higher-dimensional spherically symmetric black holes,” arXiv:2402.07574 [hep-th].
  75. H. Kodama and A. Ishibashi, “A Master equation for gravitational perturbations of maximally symmetric black holes in higher dimensions,” Prog. Theor. Phys. 110 (2003) 701–722, arXiv:hep-th/0305147.
  76. A. Ishibashi and H. Kodama, “Stability of higher dimensional Schwarzschild black holes,” Prog. Theor. Phys. 110 (2003) 901–919, arXiv:hep-th/0305185.
  77. T. Hadad, B. Kol, and M. Smolkin, “Gravito-magnetic Polarization of Schwarzschild Black Hole,” arXiv:2402.16172 [hep-th].
  78. 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].
  79. 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].
  80. D. Pereñiguez, “Black hole perturbations and electric-magnetic duality,” Phys. Rev. D 108 (2023) no. 8, 084046, arXiv:2302.10942 [gr-qc].
  81. O. J. C. Dias, M. Godazgar, and J. E. Santos, “Eigenvalue repulsions and quasinormal mode spectra of Kerr-Newman: an extended study,” JHEP 07 (2022) 076, arXiv:2205.13072 [gr-qc].
  82. P. Pani, E. Berti, and L. Gualtieri, “Scalar, Electromagnetic and Gravitational Perturbations of Kerr-Newman Black Holes in the Slow-Rotation Limit,” Phys. Rev. D 88 (2013) 064048, arXiv:1307.7315 [gr-qc].
  83. G. Cui, Y. Gao, H. H. Rugh, and L. Tan, “Rational maps as Schwarzian primitives,” Science China Mathematics 59 (2016) 1267–1284. http://dx.doi.org/10.1007/s11425-016-5140-7.
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Authors (2)

  1. Mudit Rai
  2. Luca Santoni

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