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Regularizing parametrized black hole spacetimes with Kerr symmetries

Kent Yagi1, Samantha Lomuscio1,2, Tristen Lowrey1, and Zack Carson1

  • 1Department of Physics, University of Virginia, P.O. Box 400714, Charlottesville, Virginia 22904-4714, USA
  • 2Applied Physics Laboratory, Johns Hopkins University, Laurel, Maryland 20723-6099, USA

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Phys. Rev. D 109, 044017 – Published 5 February, 2024

DOI: https://doi.org/10.1103/PhysRevD.109.044017

Abstract

Parametrized Kerr spacetimes allow us to test the nature of black holes in model-independent ways. Such spacetimes contain several arbitrary functions and, as a matter of practicality, one Taylor expands them about infinity and keeps only to finite orders in the expansion. In this paper, we focus on the parametrized spacetime preserving Killing symmetries of a Kerr spacetime and show that an unphysical divergence may appear in the metric if such a truncation is performed in the series expansion. To remedy this, we redefine the arbitrary functions so that the divergence disappears, at least for several known black hole solutions that can be mapped to the parametrized Kerr spacetime. We propose two restricted classes of the refined parametrized Kerr spacetime that only contain one or two arbitrary functions and yet can reproduce exactly all the example black hole spacetimes considered in this paper. The Petrov class of the parametrized Kerr spacetime is of type I while that for the restricted class with one arbitrary function remains type D. We also compute the ringdown frequencies and the shapes of black hole shadows for the parametrized spacetime and show how they deviate from Kerr. The refined black hole metrics with Kerr symmetries presented here are practically more useful than those proposed in previous literature.

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References (94)

  1. C. M. Will, The confrontation between general relativity and experiment, Living Rev. Relativity 17, 4 (2014).
  2. C. M. Will, Theory and Experiment in Gravitational Physics (Cambridge University Press, Cambridge, UK, 1993), pp. 396.
  3. I. H. Stairs, Testing general relativity with pulsar timing, Living Rev. Relativity 6, 5 (2003).
  4. N. Wex, Testing relativistic gravity with radio pulsars, arXiv:1402.5594.
  5. B. P. Abbott et al. (Virgo and LIGO Scientific Collaborations), Tests of general relativity with GW150914, Phys. Rev. Lett. 116, 221101 (2016).
  6. N. Yunes, K. Yagi, and F. Pretorius, Theoretical physics implications of the binary black-hole mergers GW150914 and GW151226, Phys. Rev. D 94, 084002 (2016).
  7. E. Berti, K. Yagi, and N. Yunes, Extreme gravity tests with gravitational waves from compact binary coalescences: (I) Inspiral-merger, Gen. Relativ. Gravit. 50, 46 (2018).
  8. E. Berti, K. Yagi, H. Yang, and N. Yunes, Extreme gravity tests with gravitational waves from compact binary coalescences: (II) Ringdown, Gen. Relativ. Gravit. 50, 49 (2018).
  9. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Tests of general relativity with the binary black hole signals from the LIGO-Virgo catalog GWTC-1, Phys. Rev. D 100, 104036 (2019).
  10. R. Abbott et al. (LIGO Scientific and Virgo Collaborations), Tests of general relativity with binary black holes from the second LIGO-Virgo gravitational-wave transient catalog, Phys. Rev. D 103, 122002 (2021).
  11. R. Abbott et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), Tests of general relativity with GWTC-3, arXiv:2112.06861.
  12. D. Psaltis et al. (Event Horizon Telescope Collaboration), Gravitational test beyond the first post-Newtonian order with the shadow of the M87 black hole, Phys. Rev. Lett. 125, 141104 (2020).
  13. D. Psaltis, C. Talbot, E. Payne, and I. Mandel, Probing the black hole metric. I. Black hole shadows and binary black-hole inspirals, Phys. Rev. D 103, 104036 (2021).
  14. K. Akiyama et al. (Event Horizon Telescope Collaboration), First Sagittarius A* Event Horizon Telescope Results. VI. Testing the black hole metric, Astrophys. J. Lett. 930, L17 (2022).
  15. S. Vagnozzi et al., Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A, Classical Quantum Gravity 40, 165007 (2023).
  16. W. Israel, Event horizons in static vacuum space-times, Phys. Rev. 164, 1776 (1967).
  17. S. W. Hawking, Black holes in general relativity, Commun. Math. Phys. 25, 152 (1972).
  18. V. Cardoso and P. Pani, Testing the nature of dark compact objects: A status report, Living Rev. Relativity 22, 4 (2019).
  19. C. M. Will, Testing the general relativistic “no-hair” theorems using the galactic center black hole sagittarius a*, Astrophys. J. 674, L25 (2008).
  20. D. Merritt, T. Alexander, S. Mikkola, and C. M. Will, Testing properties of the galactic center black hole using stellar orbits, Phys. Rev. D 81, 062002 (2010).
  21. L. Sadeghian and C. M. Will, Testing the black hole no-hair theorem at the galactic center: Perturbing effects of stars in the surrounding cluster, Classical Quantum Gravity 28, 225029 (2011).
  22. L. Kong, Z. Li, and C. Bambi, Constraints on the spacetime geometry around 10 stellar-mass black hole candidates from the disk’s thermal spectrum, Astrophys. J. 797, 78 (2014).
  23. C. Bambi, Note on the Cardoso-Pani-Rico parametrization to test the Kerr black hole hypothesis, Phys. Rev. D 90, 047503 (2014).
  24. J. Jiang, C. Bambi, and J. F. Steiner, Testing the Kerr nature of black hole candidates using iron line spectra in the CPR framework, Astrophys. J. 811, 130 (2015).
  25. J. Jiang, C. Bambi, and J. F. Steiner, Testing the Kerr nature of black hole candidates using iron line reverberation mapping in the Cardoso-Pani-Rico framework, Phys. Rev. D 93, 123008 (2016).
  26. Y. Xu, S. Nampalliwar, A. B. Abdikamalov, D. Ayzenberg, C. Bambi, T. Dauser, J. A. Garcia, and J. Jiang, A study of the strong gravity region of the black hole in GS 1354–645, Astrophys. J. 865, 134 (2018).
  27. N. V. Krishnendu, K. G. Arun, and C. K. Mishra, Testing the binary black hole nature of a compact binary coalescence, Phys. Rev. Lett. 119, 091101 (2017).
  28. M. Isi, M. Giesler, W. M. Farr, M. A. Scheel, and S. A. Teukolsky, Testing the no-hair theorem with GW150914, Phys. Rev. Lett. 123, 111102 (2019).
  29. C. D. Capano, M. Cabero, J. Westerweck, J. Abedi, S. Kastha, A. H. Nitz, Y.-F. Wang, A. B. Nielsen, and B. Krishnan, A multimode quasi-normal spectrum from a perturbed black hole, Phys. Rev. Lett. 131, 221402 (2023).
  30. R. Cotesta, G. Carullo, E. Berti, and V. Cardoso, Analysis of ringdown overtones in GW150914, Phys. Rev. Lett. 129, 111102 (2022).
  31. E. Finch and C. J. Moore, Searching for a ringdown overtone in GW150914, Phys. Rev. D 106, 043005 (2022).
  32. S. Ma, L. Sun, and Y. Chen, Using rational filters to uncover the first ringdown overtone in GW150914, Phys. Rev. D 107, 084010 (2023).
  33. Y.-F. Wang, C. D. Capano, J. Abedi, S. Kastha, B. Krishnan, A. B. Nielsen, A. H. Nitz, and J. Westerweck, A frequency-domain perspective on GW150914 ringdown overtone, arXiv:2310.19645.
  34. N. A. Collins and S. A. Hughes, Towards a formalism for mapping the spacetimes of massive compact objects: Bumpy black holes and their orbits, Phys. Rev. D 69, 124022 (2004).
  35. S. J. Vigeland and S. A. Hughes, Spacetime and orbits of bumpy black holes, Phys. Rev. D 81, 024030 (2010).
  36. S. J. Vigeland, Multipole moments of bumpy black holes, Phys. Rev. D 82, 104041 (2010).
  37. S. Vigeland, N. Yunes, and L. Stein, Bumpy black holes in alternate theories of gravity, Phys. Rev. D 83, 104027 (2011).
  38. K. Glampedakis and S. Babak, Mapping spacetimes with LISA: Inspiral of a test-body in a ‘quasi-Kerr’ field, Classical Quantum Gravity 23, 4167 (2006).
  39. T. Johannsen and D. Psaltis, A metric for rapidly spinning black holes suitable for strong-field tests of the no-hair theorem, Phys. Rev. D 83, 124015 (2011).
  40. T. Johannsen, Regular black hole metric with three constants of motion, Phys. Rev. D 88, 044002 (2013).
  41. Z. Carson and K. Yagi, Asymptotically flat, parametrized black hole metric preserving Kerr symmetries, Phys. Rev. D 101, 084030 (2020).
  42. G. O. Papadopoulos and K. D. Kokkotas, Preserving Kerr symmetries in deformed spacetimes, Classical Quantum Gravity 35, 185014 (2018).
  43. G. O. Papadopoulos and K. D. Kokkotas, On Kerr black hole deformations admitting a Carter constant and an invariant criterion for the separability of the wave equation, Gen. Relativ. Gravit. 53, 21 (2021).
  44. C.-Y. Chen, Rotating black holes without Z2 symmetry and their shadow images, J. Cosmol. Astropart. Phys. 05 (2020) 040.
  45. L. Rezzolla and A. Zhidenko, New parametrization for spherically symmetric black holes in metric theories of gravity, Phys. Rev. D 90, 084009 (2014).
  46. R. Konoplya, L. Rezzolla, and A. Zhidenko, General parametrization of axisymmetric black holes in metric theories of gravity, Phys. Rev. D 93, 064015 (2016).
  47. R. A. Konoplya, Z. Stuchlík, and A. Zhidenko, Axisymmetric black holes allowing for separation of variables in the Klein-Gordon and Hamilton-Jacobi equations, Phys. Rev. D 97, 084044 (2018).
  48. R. A. Konoplya and A. Zhidenko, General parametrization of black holes: The only parameters that matter, Phys. Rev. D 101, 124004 (2020).
  49. H. C. D. L. Junior, L. C. B. Crispino, P. V. P. Cunha, and C. A. R. Herdeiro, Spinning black holes with a separable Hamilton–Jacobi equation from a modified Newman–Janis algorithm, Eur. Phys. J. C 80, 1036 (2020).
  50. H. Delaporte, A. Eichhorn, and A. Held, Parameterizations of black-hole spacetimes beyond circularity, Classical Quantum Gravity 39, 134002 (2022).
  51. J. Baines and M. Visser, Killing horizons and surface gravities for a well-behaved three-function generalization of the Kerr spacetime, Universe 9, 223 (2023).
  52. A. N. Aliev and A. E. Gumrukcuoglu, Charged rotating black holes on a 3-brane, Phys. Rev. D 71, 104027 (2005).
  53. S. A. Hayward, Formation and evaporation of regular black holes, Phys. Rev. Lett. 96, 031103 (2006).
  54. J. Bardeen, in Conference Proceedings of GR5 (Conference Proceedings, U.S.S.R., Tbilisi, 1968), p. 174.
  55. S. G. Ghosh, A nonsingular rotating black hole, Eur. Phys. J. C 75, 532 (2015).
  56. R. Kumar, S. G. Ghosh, and A. Wang, Gravitational deflection of light and shadow cast by rotating Kalb-Ramond black holes, Phys. Rev. D 101, 104001 (2020).
  57. A. Sen, Rotating charged black hole solution in heterotic string theory, Phys. Rev. Lett. 69, 1006 (1992).
  58. L. Randall and R. Sundrum, A Large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83, 3370 (1999).
  59. L. Randall and R. Sundrum, An alternative to compactification, Phys. Rev. Lett. 83, 4690 (1999).
  60. C. M. Will, The confrontation between general relativity and experiment, Living Rev. Relativity 9, 3 (2006).
  61. V. Cardoso, P. Pani, and J. Rico, On generic parametrizations of spinning black-hole geometries, Phys. Rev. D 89, 064007 (2014).
  62. E. T. Newman and A. I. Janis, Note on the Kerr spinning particle metric, J. Math. Phys. (N.Y.) 6, 915 (1965).
  63. S. P. Drake and P. Szekeres, Uniqueness of the Newman-Janis algorithm in generating the Kerr-Newman metric, Gen. Relativ. Gravit. 32, 445 (2000).
  64. H. Erbin, Janis-Newman algorithm: Generating rotating and NUT charged black holes, Universe 3, 19 (2017).
  65. H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers, and E. Herlt, Exact Solutions of Einstein’s Field Equations (Cambridge University Press, Cambridge, UK, 2003).
  66. M. Campanelli, C. O. Lousto, and Y. Zlochower, Algebraic classification of numerical spacetimes and black-hole-binary remnants, Phys. Rev. D 79, 084012 (2009).
  67. W. Kinnersley, Type D vacuum metrics, J. Math. Phys. (N.Y.) 10, 1195 (1969).
  68. Y. Guo, H. Nakajima, and W. Lin, Teukolsky-like equations in a non-vacuum axisymmetric type D spacetime, arXiv:2309.06237.
  69. M. Walker and R. Penrose, On quadratic first integrals of the geodesic equations for type [22] spacetimes, Commun. Math. Phys. 18, 265 (1970).
  70. H. O. Silva and K. Glampedakis, Eikonal quasinormal modes of black holes beyond general relativity. II. Generalized scalar-tensor perturbations, Phys. Rev. D 101, 044051 (2020).
  71. K. Glampedakis, G. Pappas, H. O. Silva, and E. Berti, Post-Kerr black hole spectroscopy, Phys. Rev. D 96, 064054 (2017).
  72. K. Glampedakis and H. O. Silva, Eikonal quasinormal modes of black holes beyond general relativity, Phys. Rev. D 100, 044040 (2019).
  73. A. K. Mishra, A. Ghosh, and S. Chakraborty, Constraining extra dimensions using observations of black hole quasi-normal modes, Eur. Phys. J. C 82, 820 (2022).
  74. A. Bryant, H. O. Silva, K. Yagi, and K. Glampedakis, Eikonal quasinormal modes of black holes beyond general relativity. III. Scalar Gauss-Bonnet gravity, Phys. Rev. D 104, 044051 (2021).
  75. T. Johannsen, Photon rings around Kerr and Kerr-like black holes, Astrophys. J. 777, 170 (2013).
  76. S.-W. Wei and Y.-X. Liu, Observing the shadow of Einstein-Maxwell-Dilaton-axion black hole, J. Cosmol. Astropart. Phys. 11 (2013) 063.
  77. F. Atamurotov, A. Abdujabbarov, and B. Ahmedov, Shadow of rotating non-Kerr black hole, Phys. Rev. D 88, 064004 (2013).
  78. M. Ghasemi-Nodehi, Z. Li, and C. Bambi, Shadows of CPR black holes and tests of the Kerr metric, Eur. Phys. J. C 75, 315 (2015).
  79. A. Abdujabbarov, M. Amir, B. Ahmedov, and S. G. Ghosh, Shadow of rotating regular black holes, Phys. Rev. D 93, 104004 (2016).
  80. Z. Younsi, A. Zhidenko, L. Rezzolla, R. Konoplya, and Y. Mizuno, New method for shadow calculations: Application to parametrized axisymmetric black holes, Phys. Rev. D 94, 084025 (2016).
  81. Y. Mizuno, Z. Younsi, C. M. Fromm, O. Porth, M. De Laurentis, H. Olivares, H. Falcke, M. Kramer, and L. Rezzolla, The current ability to test theories of gravity with black hole shadows, Nat. Astron. 2, 585 (2018).
  82. A. Narang, S. Mohanty, and A. Kumar, Test of Kerr-Sen metric with black hole observations, arXiv:2002.12786.
  83. R. A. Konoplya and A. Zhidenko, Shadows of parametrized axially symmetric black holes allowing for separation of variables, Phys. Rev. D 103, 104033 (2021).
  84. M. Zubair, M. A. Raza, and E. Maqsood, Rotating black hole in Kalb–Ramond gravity: Constraining parameters by comparison with EHT observations of Sgr A* and M87*, Phys. Dark Universe 42, 101334 (2023).
  85. N. Tsukamoto, Z. Li, and C. Bambi, Constraining the spin and the deformation parameters from the black hole shadow, J. Cosmol. Astropart. Phys. 06 (2014) 043.
  86. N. Tsukamoto, Black hole shadow in an asymptotically-flat, stationary, and axisymmetric spacetime: The Kerr-Newman and rotating regular black holes, Phys. Rev. D 97, 064021 (2018).
  87. R. Shaikh, Black hole shadow in a general rotating spacetime obtained through Newman-Janis algorithm, Phys. Rev. D 100, 024028 (2019).
  88. J. Bardeen and B. S. DeWitt, Black Holes (Gordon and Breach, New York, 1973).
  89. A. Cardenas-Avendano, S. Nampalliwar, and N. Yunes, Gravitational-wave versus X-ray tests of strong-field gravity, Classical Quantum Gravity 37, 135008 (2020).
  90. Z. Carson and K. Yagi, Probing beyond-Kerr spacetimes with inspiral-ringdown corrections to gravitational waves, Phys. Rev. D 101, 084050 (2020).
  91. S. Shashank and C. Bambi, Constraining the Konoplya-Rezzolla-Zhidenko deformation parameters III: Limits from stellar-mass black holes using gravitational-wave observations, Phys. Rev. D 105, 104004 (2022).
  92. S. Kumar, A. Chowdhuri, and A. Bhattacharyya, Prospects of detecting deviations to Kerr geometry with radiation reaction effects in EMRIs, arXiv:2311.05983.
  93. E. Contreras, J. Ovalle, and R. Casadio, Gravitational decoupling for axially symmetric systems and rotating black holes, Phys. Rev. D 103, 044020 (2021).
  94. S. Vigeland, N. Yunes, and L. Stein, Bumpy black holes in alternate theories of gravity, Phys. Rev. D 83, 104027 (2011).

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Phys. Rev. D 109, 044017– Published 5 February, 2024
  • Received 14 November 2023
  • Accepted 19 January 2024
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