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Probing fuzzballs and beyond: Model-independent tests of Kerr symmetry breaking with LISA

Pablo F. Muguruza1,2,3,* and Carlos F. Sopuerta1,2,†

  • *Contact author: pfernandez@ice.csic.es
  • †Contact author: carlos.f.sopuerta@csic.es
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Phys. Rev. D 114, L061501 – Published 15 September, 2026

DOI: https://doi.org/10.1103/xx4j-9gbh

Abstract

Gravitational waves provide a unique probe of the strong-field regime of gravity, offering access to physics beyond the classical black hole paradigm. We explore how space-based observations of extreme-mass-ratio inspirals (EMRIs) by the Laser Interferometer Space Antenna (LISA) can be used to test for departures from the Kerr geometry, and in particular for the breaking of its axial and equatorial symmetries, as expected in quantum-gravity-inspired alternatives to Kerr black holes such as the fuzzball proposal. By introducing generic multipolar deformations encoding potential symmetry breakings and performing a systematic parameter estimation analysis, we forecast LISA’s ability to constrain such departures from the Kerr geometry in the strong-field regime. We show that EMRI signals with realistic signal-to-noise ratios can constrain several higher-order multipoles of the primary, opening a new observational window onto strong-field deviations from the Kerr geometry. In particular, we find that LISA can constrain generic nonaxisymmetric mass quadrupole deformations at the 10−4–10−2 level and axisymmetric mass octupole deformations at the 10−1−100 level, providing concrete observational targets for strong-field deviations from the Kerr geometry, such as those that may arise in fuzzball and other exotic-compact-object scenarios. Our results demonstrate that precision measurements of EMRI waveforms will transform LISA into a powerful laboratory for fundamental physics and offer precise constraints on quantum-gravity-motivated models of compact objects.

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References (80)

  1. A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379, 99 (1996).
  2. J. D. Bekenstein, Black holes and entropy, Phys. Rev. D 7, 2333 (1973).
  3. S. W. Hawking, Black hole explosions, Nature (London) 248, 30 (1974).
  4. K. Skenderis and M. Taylor, Fuzzball solutions and D1-D5 microstates, Phys. Rev. Lett. 98, 071601 (2007).
  5. K. Skenderis and M. Taylor, The fuzzball proposal for black holes, Phys. Rep. 467, 117 (2008).
  6. O. Lunin and S. D. Mathur, AdS/CFT duality and the black hole information paradox, Nucl. Phys. B623, 342 (2002).
  7. O. Lunin and S. D. Mathur, Statistical interpretation of Bekenstein entropy for systems with a stretched horizon, Phys. Rev. Lett. 88, 211303 (2002).
  8. S. D. Mathur, The Fuzzball proposal for black holes: An elementary review, Fortschr. Phys. 53, 793 (2005).
  9. B. D. Chowdhury and S. D. Mathur, Radiation from the non-extremal fuzzball, Classical Quantum Gravity 25, 135005 (2008).
  10. S. D. Mathur, Tunneling into fuzzball states, Gen. Relativ. Gravit. 42, 113 (2010).
  11. B. D. Chowdhury and S. D. Mathur, Pair creation in non-extremal fuzzball geometries, Classical Quantum Gravity 25, 225021 (2008).
  12. P. Brady, G. Losurdo, and H. Shinkai, LIGO, VIRGO, and KAGRA as the International Gravitational Wave Network, in Handbook of Gravitational Wave Astronomy, edited by C. Bambi, S. Katsanevas, and K. D. Kokkotas (Springer, Singapore, 2020), pp. 1–21.
  13. B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), Tests of general relativity with GW150914, Phys. Rev. Lett. 116, 221101 (2016); 121, 129902(E) (2018).
  14. B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), Tests of general relativity with the binary black hole signals from the LIGO-Virgo catalog GWTC-1, Phys. Rev. D 100, 104036 (2019).
  15. R. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), Tests of general relativity with binary black holes from the second LIGO-Virgo gravitational-wave transient catalog, Phys. Rev. D 103, 122002 (2021).
  16. R. Abbott et al. (LIGO Scientific Collaboration, VIRGO Collaboration, and KAGRA Collaboration), Tests of general relativity with GWTC-3, Phys. Rev. D 112, 084080 (2025).
  17. A. G. Abac et al. (LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration), GW250114: Testing Hawking’s area law and the Kerr nature of black holes, Phys. Rev. Lett. 135, 111403 (2025).
  18. A. G. Abac et al. (LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration), Black hole spectroscopy and tests of general relativity with GW250114, Phys. Rev. Lett. 136, 041403 (2026).
  19. E. Berti et al., Testing general relativity with present and future astrophysical observations, Classical Quantum Gravity 32, 243001 (2015).
  20. L. Barack et al., Black holes, gravitational waves and fundamental physics: A roadmap, Classical Quantum Gravity 36, 143001 (2019).
  21. M. Punturo et al., The Einstein Telescope: A third-generation gravitational wave observatory, Classical Quantum Gravity 27, 194002 (2010).
  22. D. Reitze et al., Cosmic explorer: The U.S. contribution to gravitational-wave astronomy beyond LIGO, Bull. Am. Astron. Soc. 51, 035 (2019).
  23. B. Sathyaprakash et al., Scientific objectives of Einstein Telescope, Classical Quantum Gravity 29, 124013 (2012); 30, 079501(E) (2013).
  24. M. Maggiore et al. (ET Collaboration), Science case for the Einstein Telescope, J. Cosmol. Astropart. Phys. 03 (2019) 050.
  25. A. Abac et al. (ET Collaboration), The science of the Einstein Telescope, J. Cosmol. Astropart. Phys. 03 (2026) 081.
  26. P. Amaro-Seoane et al. (LISA Collaboration), Laser Interferometer Space Antenna, arXiv:1702.00786.
  27. M. Colpi et al., LISA definition study report, arXiv:2402.07571.
  28. P. A. Seoane et al. (LISA Collaboration), Astrophysics with the Laser Interferometer Space Antenna, Living Rev. Relativity 26, 2 (2023).
  29. P. Auclair et al. (LISA Cosmology Working Group), Cosmology with the Laser Interferometer Space Antenna, Living Rev. Relativity 26, 5 (2023).
  30. E. Barausse et al., Prospects for fundamental physics with LISA, Gen. Relativ. Gravit. 52, 81 (2020).
  31. K. G. Arun et al. (LISA Collaboration), New horizons for fundamental physics with LISA, Living Rev. Relativity 25, 4 (2022).
  32. S. Babak, J. Gair, A. Sesana, E. Barausse, C. F. Sopuerta, C. P. L. Berry, E. Berti, P. Amaro-Seoane, A. Petiteau, and A. Klein, Science with the space-based interferometer LISA. V: Extreme mass-ratio inspirals, Phys. Rev. D 95, 103012 (2017).
  33. C. P. L. Berry, S. A. Hughes, C. F. Sopuerta, A. J. K. Chua, A. Heffernan, K. Holley-Bockelmann, D. P. Mihaylov, M. C. Miller, and A. Sesana, The unique potential of extreme mass-ratio inspirals for gravitational-wave astronomy, Bull. Am. Astron. Soc. 51, 42 (2019).
  34. A. Cárdenas-Avendaño and C. F. Sopuerta, Testing gravity with extreme-mass-ratio inspirals, in Recent Progress on Gravity Tests (Springer Nature, Singapore, 2024), pp. 275–359.
  35. S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, England, 2011).
  36. R. Geroch, Multipole moments. II. Curved space, J. Math. Phys. (N.Y.) 11, 2580 (1970).
  37. R. O. Hansen, Multipole moments of stationary space-times, J. Math. Phys. (N.Y.) 15, 4652 (1974).
  38. K. S. Thorne, Multipole expansions of gravitational radiation, Rev. Mod. Phys. 52, 299 (1980).
  39. R. P. Kerr, Gravitational field of a spinning mass as an example of algebraically special metrics, Phys. Rev. Lett. 11, 237 (1963).
  40. W. Israel, Singular hypersurfaces and thin shells in general relativity, Nuovo Cimento B 44, 1 (1966); 48, 463(E) (1967).
  41. B. Carter, Axisymmetric black hole has only two degrees of freedom, Phys. Rev. Lett. 26, 331 (1971).
  42. S. W. Hawking, Black holes in general relativity, Commun. Math. Phys. 25, 152 (1972).
  43. K. Skenderis and M. Taylor, Fuzzball solutions and D1-D5 microstates, Phys. Rev. Lett. 98, 071601 (2007).
  44. V. Cardoso, S. Hopper, C. F. B. Macedo, C. Palenzuela, and P. Pani, Gravitational-wave signatures of exotic compact objects and of quantum corrections at the horizon scale, Phys. Rev. D 94, 084031 (2016).
  45. V. Cardoso and P. Pani, Testing the nature of dark compact objects: a status report, Living Rev. Relativity 22, 4 (2019).
  46. D. R. Mayerson, Fuzzballs and observations, Gen. Relativ. Gravit. 52, 115 (2020).
  47. M. Bianchi, D. Consoli, A. Grillo, J. F. Morales, P. Pani, and G. Raposo, Distinguishing fuzzballs from black holes through their multipolar structure, Phys. Rev. Lett. 125, 221601 (2020).
  48. I. Bena and D. R. Mayerson, Black holes lessons from multipole ratios, J. High Energy Phys. 03 (2021) 114.
  49. F. Bacchini, D. R. Mayerson, B. Ripperda, J. Davelaar, H. Olivares, T. Hertog, and B. Vercnocke, Fuzzball shadows: Emergent horizons from microstructure, Phys. Rev. Lett. 127, 171601 (2021).
  50. D. R. Mayerson and B. Vercnocke, Observational opportunities for the Fuzzball program, arXiv:2306.01565.
  51. S. Raju and P. Shrivastava, Critique of the Fuzzball program, Phys. Rev. D 99, 066009 (2019).
  52. F. D. Ryan, Gravitational waves from the inspiral of a compact object into a massive, axisymmetric body with arbitrary multipole moments, Phys. Rev. D 52, 5707 (1995).
  53. F. D. Ryan, Effect of gravitational radiation reaction on circular orbits around a spinning black hole, Phys. Rev. D 52, R3159 (1995).
  54. F. D. Ryan, Effect of gravitational radiation reaction on nonequatorial orbits around a Kerr black hole, Phys. Rev. D 53, 3064 (1996).
  55. F. D. Ryan, Accuracy of estimating the multipole moments of a massive body from the gravitational waves of a binary inspiral, Phys. Rev. D 56, 1845 (1997).
  56. F. D. Ryan, Scalar waves produced by a scalar charge orbiting a massive body with arbitrary multipole moments, Phys. Rev. D 56, 7732 (1997).
  57. K. Danzmann, LISA: Laser interferometer space antenna for gravitational wave measurements, Classical Quantum Gravity 13, A247 (1996).
  58. C. Cutler, Angular resolution of the LISA gravitational wave detector, Phys. Rev. D 57, 7089 (1998).
  59. T. A. Prince, M. Tinto, S. L. Larson, and J. W. Armstrong, The LISA optimal sensitivity, Phys. Rev. D 66, 122002 (2002).
  60. L. Barack and C. Cutler, LISA capture sources: Approximate waveforms, signal-to-noise ratios, and parameter estimation accuracy, Phys. Rev. D 69, 082005 (2004).
  61. L. Barack and C. Cutler, Using LISA EMRI sources to test off-Kerr deviations in the geometry of massive black holes, Phys. Rev. D 75, 042003 (2007).
  62. K. Fransen and D. R. Mayerson, Detecting equatorial symmetry breaking with LISA, Phys. Rev. D 106, 064035 (2022).
  63. N. Loutrel, R. Brito, A. Maselli, and P. Pani, Inspiraling compact objects with generic deformations, Phys. Rev. D 105, 124050 (2022).
  64. N. Loutrel, R. Brito, A. Maselli, and P. Pani, Relevance of precession for tests of the black hole no hair theorems, Phys. Rev. D 110, 044003 (2024).
  65. E. Poisson, A. Pound, and I. Vega, The motion of point particles in curved spacetime, Living Rev. Relativity 14, 7 (2011).
  66. L. Barack and A. Pound, Self-force and radiation reaction in general relativity, Rep. Prog. Phys. 82, 016904 (2019).
  67. S. A. Hughes, N. Warburton, G. Khanna, A. J. K. Chua, and M. L. Katz, Adiabatic waveforms for extreme mass-ratio inspirals via multivoice decomposition in time and frequency, Phys. Rev. D 103, 104014 (2021).
  68. M. L. Katz, A. J. K. Chua, L. Speri, N. Warburton, and S. A. Hughes, Fast extreme-mass-ratio-inspiral waveforms: New tools for millihertz gravitational-wave data analysis, Phys. Rev. D 104, 064047 (2021).
  69. L. Speri, M. L. Katz, A. J. K. Chua, S. A. Hughes, N. Warburton, J. E. Thompson, C. E. A. Chapman-Bird, and J. R. Gair, Fast and Fourier: Extreme mass ratio inspiral waveforms in the frequency domain, Front. Appl. Math. Stat. 9, 1266739 (2024).
  70. P. F. Muguruza and C. F. Sopuerta, Probing Kerr symmetry breaking with LISA extreme-mass-ratio inspirals, Phys. Rev. D 114, 064010 (2026).
  71. M. Maggiore, Gravitational Waves: Volume 1: Theory and Experiments (Oxford University Press, Oxford, 2007).
  72. C. W. Misner, K. Thorne, and J. A. Wheeler, Gravitation (W. H. Freeman & Co., San Francisco, 1973).
  73. N. J. Cornish and L. J. Rubbo, The LISA response function, Phys. Rev. D 67, 022001 (2003).
  74. J.-B. Bayle, O. Hartwig, A. Petiteau, and M. Lilley, LISANode, Zenodo (2022), 10.5281/zenodo.6461078.
  75. C. F. B. Macedo, P. Pani, V. Cardoso, and L. C. B. Crispino, Astrophysical signatures of boson stars: Quasinormal modes and inspiral resonances, Phys. Rev. D 88, 064046 (2013).
  76. K. Destounis, F. Angeloni, M. Vaglio, and P. Pani, Extreme-mass-ratio inspirals into rotating boson stars: Nonintegrability, chaos, and transient resonances, Phys. Rev. D 108, 084062 (2023).
  77. M. Bianchi, D. Bini, and G. Di Russo, Scalar waves in a topological star spacetime: Self-force and radiative losses, Phys. Rev. D 111, 044017 (2025).
  78. G. Di Russo, M. Bianchi, and D. Bini, Scalar waves from unbound orbits in a topological star spacetime: PN reconstruction of the field and radiation losses in a self-force approach, Phys. Rev. D 112, 024002 (2025).
  79. M. Melis, R. Brito, and P. Pani, Extreme mass ratio inspirals around topological stars, Phys. Rev. D 111, 124043 (2025).
  80. N. Afshordi et al. (LISA Consortium Waveform Working Group), Waveform modelling for the Laser Interferometer Space Antenna, Living Rev. Relativity 28, 9 (2025).

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Phys. Rev. D 114, L061501– Published 15 September, 2026
  • Received 10 April 2026
  • Accepted 13 August 2026
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