- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Efficient waveforms for asymmetric-mass eccentric equatorial inspirals into rapidly spinning black holes

Christian E. A. Chapman-Bird1,2,*, Lorenzo Speri3, Zachary Nasipak4, Ollie Burke2,5, Michael L. Katz6, Alessandro Santini7, Shubham Kejriwal8, Philip Lynch7, Josh Mathews8 et al.

Hassan Khalvati9,10, Jonathan E. Thompson4,11, Soichiro Isoyama8, Scott A. Hughes12, Niels Warburton13, Alvin J. K. Chua8,14, and Maxime Pigou5

  • *Contact author: c.chapman-bird@bham.ac.uk
PDF

Phys. Rev. D 112, 104023 – Published 12 November, 2025

DOI: https://doi.org/10.1103/scbp-75pf

Abstract

Observations of gravitational-wave signals emitted by compact binary inspirals provide unique insights into their properties, but their analysis requires accurate and efficient waveform models. Intermediate- and extreme-mass-ratio inspirals (I/EMRIs), with mass ratios q≳102, are promising sources for future detectors such as the Laser Interferometer Space Antenna (LISA). Modeling waveforms for these asymmetric-mass binaries is challenging, entailing the tracking of many harmonic modes over thousands to millions of cycles. The FastEMRIWaveforms (few) modeling framework addresses this need, leveraging precomputation of mode data and interpolation to rapidly compute adiabatic waveforms for eccentric inspirals into zero-spin black holes. In this work, we extend few to model eccentric equatorial inspirals into black holes with spin magnitudes |a|≤0.999. Our model supports eccentricities e≤0.9 and semilatus recta p≤200, enabling the generation of long-duration IMRI waveforms, and produces waveforms in ∼100  ms with hardware acceleration. Characterizing systematic errors, we estimate that our model attains mismatches of ∼10−5 (for LISA sensitivity) with respect to error-free adiabatic waveforms over the majority of the parameter space. We find that kludge models can introduce errors in signal-to-noise ratios (SNRs) as great as  −40%+60% and induce marginal biases of up to ∼1σ in parameter estimation. We show that LISA’s horizon redshift for I/EMRI signals varies significantly with a, reaching a redshift of 3 (15) for EMRIs (IMRIs) with only minor (∼10%) dependence on e for an SNR threshold of 20. For signals with SNR∼50, spin and eccentricity at plunge are measured with uncertainties of δa∼10−7 and δef∼10−5. This work advances the state of the art in waveform generation for asymmetric-mass binaries, providing open-source tools for the investigation of I/EMRI astrophysics and data analysis.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (333)

  1. R. Abbott et al., GWTC-3: Compact binary coalescences observed by LIGO and Virgo during the second part of the third observing run, Phys. Rev. X 13, 041039 (2023).
  2. J. Aasi et al., Advanced LIGO, Classical Quantum Gravity 32, 074001 (2015).
  3. F. Acernese et al., Advanced Virgo: A second-generation interferometric gravitational wave detector, Classical Quantum Gravity 32, 024001 (2015).
  4. T. Akutsu et al., KAGRA: 2.5 generation interferometric gravitational wave detector, Nat. Astron. 3, 35 (2019).
  5. R. Abbott et al., Population of merging compact binaries inferred using gravitational waves through GWTC-3, Phys. Rev. X 13, 011048 (2023).
  6. V. Varma, S. E. Field, M. A. Scheel, J. Blackman, D. Gerosa, L. C. Stein, L. E. Kidder, and H. P. Pfeiffer, Surrogate models for precessing binary black hole simulations with unequal masses, Phys. Rev. Res. 1, 033015 (2019).
  7. A. Ramos-Buades, A. Buonanno, H. Estellés, M. Khalil, D. P. Mihaylov, S. Ossokine, L. Pompili, and M. Shiferaw, Next generation of accurate and efficient multipolar precessing-spin effective-one-body waveforms for binary black holes, Phys. Rev. D 108, 124037 (2023).
  8. G. Pratten et al., Computationally efficient models for the dominant and subdominant harmonic modes of precessing binary black holes, Phys. Rev. D 103, 104056 (2021).
  9. N. Afshordi et al., Waveform modelling for the laser interferometer space antenna, arXiv:2311.01300.
  10. R. Abbott et al., GW190814: Gravitational waves from the coalescence of a 23 solar mass black hole with a 2.6 solar mass compact object, Astrophys. J. Lett. 896, L44 (2020).
  11. A. G. Abac et al., Observation of gravitational waves from the coalescence of a 2.5–4.5M⊙ compact object and a neutron star, Astrophys. J. Lett. 970, L34 (2024).
  12. R. Abbott et al., GW190412: Observation of a binary-black-hole coalescence with asymmetric masses, Phys. Rev. D 102, 043015 (2020).
  13. M. Punturo et al., The Einstein telescope: A third-generation gravitational wave observatory, Classical Quantum Gravity 27, 194002 (2010).
  14. D. Reitze et al., Cosmic explorer: The U.S. contribution to gravitational-wave astronomy beyond LIGO, Bull. Am. Astron. Soc. 51, 035 (2019).
  15. M. A. Sedda et al., The missing link in gravitational-wave astronomy: Discoveries waiting in the decihertz range, Classical Quantum Gravity 37, 215011 (2020).
  16. N. Seto, S. Kawamura, and T. Nakamura, Possibility of direct measurement of the acceleration of the universe using 0.1-Hz band laser interferometer gravitational wave antenna in space, Phys. Rev. Lett. 87, 221103 (2001).
  17. T. Nakamura et al., Pre-DECIGO can get the smoking gun to decide the astrophysical or cosmological origin of GW150914-like binary black holes, Prog. Theor. Exp. Phys. 2016, 093E01 (2016).
  18. S. Kawamura et al., Current status of space gravitational wave antenna DECIGO and B-DECIGO, Prog. Theor. Exp. Phys. 2021, 05A105 (2021).
  19. M. Branchesi et al., Lunar gravitational-wave detection, Space Sci. Rev. 219, 67 (2023).
  20. P. Amaro-Seoane, J. R. Gair, M. Freitag, M. Coleman Miller, I. Mandel, C. J. Cutler, and S. Babak, Astrophysics, detection and science applications of intermediate- and extreme mass-ratio inspirals, Classical Quantum Gravity 24, R113 (2007).
  21. M. Colpi et al., LISA definition study report, arXiv:2402.07571.
  22. J. Mei et al., The TianQin project: Current progress on science and technology, Prog. Theor. Exp. Phys. 2021, 05A107 (2021).
  23. Z. Luo, Y. Wang, Y. Wu, W. Hu, and G. Jin, The Taiji program: A concise overview, Prog. Theor. Exp. Phys. 2021, 05A108 (2021).
  24. Y. Gong, J. Luo, and B. Wang, Concepts and status of Chinese space gravitational wave detection projects, Nat. Astron. 5, 881 (2021).
  25. P. Amaro-Seoane, Relativistic dynamics and extreme mass ratio inspirals, Living Rev. Relativity 21, 4 (2018).
  26. Pau Amaro-Seoane, Extremely large mass-ratio inspirals, Phys. Rev. D 99, 123025 (2019).
  27. E. Gourgoulhon, A. Le Tiec, F. H. Vincent, and N. Warburton, Gravitational waves from bodies orbiting the Galactic Center black hole and their detectability by LISA, Astron. Astrophys. 627, A92 (2019).
  28. 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).
  29. 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).
  30. L. Barack and C. Cutler, LISA capture sources: Approximate waveforms, signal-to-noise ratios, and parameter estimation accuracy, Phys. Rev. D 69, 082005 (2004).
  31. J. R. Gair, M. Vallisneri, S. L. Larson, and J. G. Baker, Testing general relativity with low-frequency, space-based gravitational-wave detectors, Living Rev. Relativity 16, 7 (2013).
  32. A. Maselli, N. Franchini, L. Gualtieri, and T. P. Sotiriou, Detecting scalar fields with extreme mass ratio inspirals, Phys. Rev. Lett. 125, 141101 (2020).
  33. A. Maselli, N. Franchini, L. Gualtieri, T. P. Sotiriou, S. Barsanti, and P. Pani, Detecting fundamental fields with LISA observations of gravitational waves from extreme mass-ratio inspirals, Nat. Astron. 6, 464 (2022).
  34. S. Barsanti, N. Franchini, L. Gualtieri, A. Maselli, and T. P. Sotiriou, Extreme mass-ratio inspirals as probes of scalar fields: Eccentric equatorial orbits around Kerr black holes, Phys. Rev. D 106, 044029 (2022).
  35. L. Speri, S. Barsanti, A. Maselli, T. P. Sotiriou, N. Warburton, M. van de Meent, A. J. K. Chua, O. Burke, and J. Gair, Probing fundamental physics with extreme mass ratio inspirals: A full Bayesian inference for scalar charge, arXiv:2406.07607.
  36. B. Bonga, H. Yang, and S. A. Hughes, Tidal resonance in extreme mass-ratio inspirals, Phys. Rev. Lett. 123, 101103 (2019).
  37. H. Yang, B. Bonga, Z. Peng, and G. Li, Relativistic mean motion resonance, Phys. Rev. D 100, 124056 (2019).
  38. Y. Yin, J. Mathews, A. J. K. Chua, and X. Chen, Relativistic model of binary extreme-mass-ratio inspiral systems and their gravitational radiation, Phys. Rev. D 111, 103007 (2025).
  39. C. Dyson, T. F. M. Spieksma, R. Brito, M. van de Meent, and S. Dolan, Environmental effects in extreme-mass-ratio inspirals: Perturbations to the environment in Kerr spacetimes, Phys. Rev. Lett. 134, 211403 (2025).
  40. L. Speri, A. Antonelli, L. Sberna, S. Babak, E. Barausse, J. R. Gair, and M. L. Katz, Probing accretion physics with gravitational waves, Phys. Rev. X 13, 021035 (2023).
  41. J. R. Gair, C. Tang, and M. Volonteri, LISA extreme-mass-ratio inspiral events as probes of the black hole mass function, Phys. Rev. D 81, 104014 (2010).
  42. C. E. A. Chapman-Bird, C. P. L. Berry, and G. Woan, Rapid determination of LISA sensitivity to extreme mass ratio inspirals with machine learning, Mon. Not. R. Astron. Soc. 522, 6043 (2023).
  43. E. Barausse, L. Rezzolla, D. Petroff, and M. Ansorg, Gravitational waves from extreme mass ratio inspirals in non-pure Kerr spacetimes, Phys. Rev. D 75, 064026 (2007).
  44. E. Barausse and L. Rezzolla, The influence of the hydrodynamic drag from an accretion torus on extreme mass-ratio inspirals, Phys. Rev. D 77, 104027 (2008).
  45. N. Yunes, B. Kocsis, A. Loeb, and Z. Haiman, Imprint of accretion disk-induced migration on gravitational waves from extreme mass ratio inspirals, Phys. Rev. Lett. 107, 171103 (2011).
  46. E. Barausse, V. Cardoso, and P. Pani, Can environmental effects spoil precision gravitational-wave astrophysics?, Phys. Rev. D 89, 104059 (2014).
  47. E. Barausse, V. Cardoso, and P. Pani, Environmental effects for gravitational-wave astrophysics, J. Phys. Conf. Ser. 610, 012044 (2015).
  48. H. Khalvati, A. Santini, F. Duque, L. Speri, J. Gair, H. Yang, and R. Brito, Impact of relativistic waveforms in LISA’s science objectives with extreme-mass-ratio inspirals, Phys. Rev. D 111, 082010 (2025).
  49. F. Duque, S. Kejriwal, L. Sberna, L. Speri, and J. Gair, Constraining accretion physics with gravitational waves from eccentric extreme-mass-ratio inspirals, Phys. Rev. D 111, 084006 (2025).
  50. L. Copparoni, E. Barausse, L. Speri, L. Sberna, and A. Derdzinski, Implications of stochastic gas torques for asymmetric binaries in the LISA band, Phys. Rev. D 111, 104079 (2025).
  51. Z. Pan, Z. Lyu, and H. Yang, Wet extreme mass ratio inspirals may be more common for spaceborne gravitational wave detection, Phys. Rev. D 104, 063007 (2021).
  52. Z. Pan and H. Yang, Formation rate of extreme mass ratio inspirals in active galactic nuclei, Phys. Rev. D 103, 103018 (2021).
  53. P. A. Seoane et al., Astrophysics with the laser interferometer space antenna, Living Rev. Relativity 26, 2 (2023).
  54. S. Naoz, S. C. Rose, E. Michaely, D. Melchor, E. Ramirez-Ruiz, B. Mockler, and J. D. Schnittman, The combined effects of two-body relaxation processes and the eccentric Kozai–Lidov mechanism on the extreme-mass-ratio inspirals rate, Astrophys. J. Lett. 927, L18 (2022).
  55. C. L. MacLeod and C. J. Hogan, Precision of Hubble constant derived using black hole binary absolute distances and statistical redshift information, Phys. Rev. D 77, 043512 (2008).
  56. D. Laghi, N. Tamanini, W. Del Pozzo, A. Sesana, J. Gair, S. Babak, and D. Izquierdo-Villalba, Gravitational-wave cosmology with extreme mass-ratio inspirals, Mon. Not. R. Astron. Soc. 508, 4512 (2021).
  57. C. Liu, D. Laghi, and N. Tamanini, Probing modified gravitational-wave propagation with extreme mass-ratio inspirals, Phys. Rev. D 109, 063521 (2024).
  58. P. Auclair et al., Cosmology with the laser interferometer space antenna, Living Rev. Relativity 26, 5 (2023).
  59. M. Toscani, O. Burke, C. Liu, N. B. Zamel, N. Tamanini, and F. Pozzoli, Strongly lensed extreme mass-ratio inspirals, Phys. Rev. D 109, 063505 (2024).
  60. E. Savalle, J. Gair, L. Speri, and S. Babak, Assessing the impact of instrumental calibration uncertainty on LISA science, Phys. Rev. D 106, 022003 (2022).
  61. A. Pound and B. Wardell, Black hole perturbation theory and gravitational self-force, in Handbook of Gravitational Wave Astronomy (Springer, Singapore, 2022), pp. 1411–1530.
  62. L. Barack and A. Pound, Self-force and radiation reaction in general relativity, Rep. Prog. Phys. 82, 016904 (2019).
  63. L. Barack, Gravitational self force in extreme mass-ratio inspirals, Classical Quantum Gravity 26, 213001 (2009).
  64. T. Alexander, EMRIs and the relativistic loss-cone: The curious case of the fortunate coincidence, J. Phys. Conf. Ser. 840, 012019 (2017).
  65. W. Schmidt, Celestial mechanics in Kerr space-time, Classical Quantum Gravity 19, 2743 (2002).
  66. 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); 107, 089901(E) (2023).
  67. S. Drasco and S. A. Hughes, Gravitational wave snapshots of generic extreme mass ratio inspirals, Phys. Rev. D 73, 024027 (2006); 88, 109905(E) (2013); 90, 109905(E) (2014).
  68. C. O. Lousto and J. Healy, Exploring the small mass ratio binary black hole merger via Zeno’s dichotomy approach, Phys. Rev. Lett. 125, 191102 (2020).
  69. N. Rosato, J. Healy, and C. O. Lousto, Adapted gauge to small mass ratio binary black hole evolutions, Phys. Rev. D 103, 104068 (2021).
  70. C. O. Lousto and J. Healy, Study of the intermediate mass ratio black hole binary merger up to 1000∶1 with numerical relativity, Classical Quantum Gravity 40, 09LT01 (2023).
  71. N. A. Wittek, A. Pound, H. P. Pfeiffer, and L. Barack, Worldtube excision method for intermediate-mass-ratio inspirals: Self-consistent evolution in a scalar-charge model, Phys. Rev. D 110, 084023 (2024).
  72. N. A. Wittek, L. Barack, H. P. Pfeiffer, A. Pound, N. Deppe, L. E. Kidder, A. Macedo, K. C. Nelli, W. Throwe, and N. L. Vu, Relieving scale disparity in binary black hole simulations, arXiv:2410.22290.
  73. M. L. Katz, N. Karnesis, N. Korsakova, J. R. Gair, and N. Stergioulas, Efficient GPU-accelerated multisource global fit pipeline for LISA data analysis, Phys. Rev. D 111, 024060 (2025).
  74. S. Deng, S. Babak, M. Le Jeune, S. Marsat, E. Plagnol, and A. Sartirana, Modular global-fit pipeline for LISA data analysis, Phys. Rev. D 111, 103014 (2025).
  75. T. B. Littenberg and N. J. Cornish, Prototype global analysis of LISA data with multiple source types, Phys. Rev. D 107, 063004 (2023).
  76. Y. Mino, M. Sasaki, and T. Tanaka, Gravitational radiation reaction to a particle motion, Phys. Rev. D 55, 3457 (1997).
  77. T. C. Quinn and R. M. Wald, An axiomatic approach to electromagnetic and gravitational radiation reaction of particles in curved space-time, Phys. Rev. D 56, 3381 (1997).
  78. S. E. Gralla and R. M. Wald, A rigorous derivation of gravitational self-force, Classical Quantum Gravity 25, 205009 (2008).
  79. S. Detweiler, Gravitational radiation reaction and second order perturbation theory, Phys. Rev. D 85, 044048 (2012).
  80. S. E. Gralla, Second order gravitational self force, Phys. Rev. D 85, 124011 (2012).
  81. A. Pound, Second-order gravitational self-force, Phys. Rev. Lett. 109, 051101 (2012).
  82. A. I. Harte, Motion in classical field theories and the foundations of the self-force problem, Fund. Theor. Phys. 179, 327 (2015).
  83. E. Poisson, A. Pound, and I. Vega, The motion of point particles in curved spacetime, Living Rev. Relativity 14, 7 (2011).
  84. T. Hinderer and E. E. Flanagan, Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital motion, Phys. Rev. D 78, 064028 (2008).
  85. J. Miller and A. Pound, Two-timescale evolution of extreme-mass-ratio inspirals: Waveform generation scheme for quasicircular orbits in Schwarzschild spacetime, Phys. Rev. D 103, 064048 (2021).
  86. J. Mathews and A. Pound, Post-adiabatic waveform-generation framework for asymmetric precessing binaries, arXiv:2501.01413.
  87. N. Yunes, A. Buonanno, S. A. Hughes, Y. Pan, E. Barausse, M. C. Miller, and W. Throwe, Extreme mass-ratio inspirals in the effective-one-body approach: Quasi-circular, equatorial orbits around a spinning black hole, Phys. Rev. D 83, 044044 (2011); 88, 109904(E) (2013).
  88. D. Chiaramello and A. Nagar, Faithful analytical effective-one-body waveform model for spin-aligned, moderately eccentric, coalescing black hole binaries, Phys. Rev. D 101, 101501 (2020).
  89. C. Zhang, W.-B. Han, and S.-C. Yang, Analytical effective one-body formalism for extreme-mass-ratio inspirals with eccentric orbits, Commun. Theor. Phys. 73, 085401 (2021).
  90. A. Ramos-Buades, A. Buonanno, M. Khalil, and S. Ossokine, Effective-one-body multipolar waveforms for eccentric binary black holes with nonprecessing spins, Phys. Rev. D 105, 044035 (2022).
  91. C. Zhang, W.-B. Han, X.-Y. Zhong, and G. Wang, Geometrized effective-one-body formalism for extreme-mass-ratio limits: Generic orbits, Phys. Rev. D 104, 024050 (2021).
  92. S. Albanesi, A. Nagar, and S. Bernuzzi, Effective one-body model for extreme-mass-ratio spinning binaries on eccentric equatorial orbits: Testing radiation reaction and waveform, Phys. Rev. D 104, 024067 (2021).
  93. A. Nagar and S. Albanesi, Toward a gravitational self-force-informed effective-one-body waveform model for nonprecessing, eccentric, large-mass-ratio inspirals, Phys. Rev. D 106, 064049 (2022).
  94. A. Albertini, A. Nagar, A. Pound, N. Warburton, B. Wardell, L. Durkan, and J. Miller, Comparing second-order gravitational self-force and effective one body waveforms from inspiralling, quasicircular and nonspinning black hole binaries. II. The large-mass-ratio case, Phys. Rev. D 106, 084062 (2022).
  95. A. Albertini, R. Gamba, A. Nagar, and S. Bernuzzi, Effective-one-body waveforms for extreme-mass-ratio binaries: Consistency with second-order gravitational self-force quasicircular results and extension to nonprecessing spins and eccentricity, Phys. Rev. D 109, 044022 (2024).
  96. S. Albanesi, S. Bernuzzi, T. Damour, A. Nagar, and A. Placidi, Faithful effective-one-body waveform of small-mass-ratio coalescing black hole binaries: The eccentric, nonspinning case, Phys. Rev. D 108, 084037 (2023).
  97. C. Cheung, J. Parra-Martinez, I. Z. Rothstein, N. Shah, and J. Wilson-Gerow, Effective field theory for extreme mass ratio binaries, Phys. Rev. Lett. 132, 091402 (2024).
  98. A. Gamboa et al., Accurate waveforms for eccentric, aligned-spin binary black holes: The multipolar effective-one-body model SEOBNRv5EHM, arXiv:2412.12823.
  99. N. Loutrel, S. Mukherjee, A. Maselli, and P. Pani, Analytical model of precessing binaries using post-Newtonian theory in the extreme mass-ratio limit: General formalism, Phys. Rev. D 110, 024006 (2024).
  100. K. Paul, A. Maurya, Q. Henry, K. Sharma, P. Satheesh, Divyajyoti, P. Kumar, and C. K. Mishra, Eccentric, spinning, inspiral-merger-ringdown waveform model with higher modes for the detection and characterization of binary black holes, Phys. Rev. D 111, 084074 (2025).
  101. C. Cheung, J. Parra-Martinez, I. Z. Rothstein, N. Shah, and J. Wilson-Gerow, Gravitational scattering and beyond from extreme mass ratio effective field theory, J. High Energy Phys. 10 (2024) 005.
  102. D. Akpinar, V. del Duca, and R. Gonzo, The spinning self-force EFT: 1SF waveform recursion relation and Compton scattering, arXiv:2504.02025.
  103. G. Morras, G. Pratten, and P. Schmidt, Improved post-Newtonian waveform model for inspiralling precessing-eccentric compact binaries, Phys. Rev. D 111, 084052 (2025).
  104. M. d. L. Planas, A. Ramos-Buades, C. García-Quirós, H. Estellés, S. Husa, and M. Haney, Time-domain phenomenological multipolar waveforms for aligned-spin binary black holes in elliptical orbits, arXiv:2503.13062.
  105. I. Strusberg, B. Rom, and R. Sari, Universal Waveforms for Extreme Mass-Ratio Inspiral, arXiv:2505.07941.
  106. A. Apte and S. A. Hughes, Exciting black hole modes via misaligned coalescences: I. Inspiral, transition, and plunge trajectories using a generalized Ori-Thorne procedure, Phys. Rev. D 100, 084031 (2019).
  107. L. Küchler, G. Compère, L. Durkan, and A. Pound, Self-force framework for transition-to-plunge waveforms, SciPost Phys. 17, 056 (2024).
  108. D. R. Becker and S. A. Hughes, Transition from adiabatic inspiral to plunge for eccentric binaries, Phys. Rev. D 111, 064003 (2025).
  109. G. Lhost and G. Compère, Approach to the separatrix with eccentric orbits, arXiv:2412.04249.
  110. L. Küchler, G. Compère, and A. Pound, Self-force framework for merger-ringdown waveforms, arXiv:2506.02189.
  111. B. Carter, Global structure of the Kerr family of gravitational fields, Phys. Rev. 174, 1559 (1968).
  112. Y. Mino, Perturbative approach to an orbital evolution around a supermassive black hole, Phys. Rev. D 67, 084027 (2003).
  113. S. Drasco, E. E. Flanagan, and S. A. Hughes, Computing inspirals in Kerr in the adiabatic regime. I. The scalar case, Classical Quantum Gravity 22, S801 (2005).
  114. N. Sago, T. Tanaka, W. Hikida, K. Ganz, and H. Nakano, The adiabatic evolution of orbital parameters in the Kerr spacetime, Prog. Theor. Phys. 115, 873 (2006).
  115. T. Tanaka, Gravitational radiation reaction, Prog. Theor. Phys. Suppl. 163, 120 (2006).
  116. S. Isoyama, R. Fujita, H. Nakano, N. Sago, and T. Tanaka, “Flux-balance formulae” for extreme mass-ratio inspirals, Prog. Theor. Exp. Phys. 2019, 013E01 (2019).
  117. A. M. Grant, Flux-balance laws for spinning bodies under the gravitational self-force, Phys. Rev. D 111, 084015 (2025).
  118. S. A. Hughes, Evolution of circular, nonequatorial orbits of Kerr black holes due to gravitational wave emission. II. Inspiral trajectories and gravitational wave forms, Phys. Rev. D 64, 064004 (2001); 88, 109902(E) (2013).
  119. L. S. Finn and K. S. Thorne, Gravitational waves from a compact star in a circular, inspiral orbit, in the equatorial plane of a massive, spinning black hole, as observed by LISA, Phys. Rev. D 62, 124021 (2000).
  120. Y. Mino, Adiabatic expansion for metric perturbation and the condition to solve the gauge problem for gravitational radiation reaction problem, Prog. Theor. Phys. 115, 43 (2006).
  121. P. A. Sundararajan, G. Khanna, S. A. Hughes, and S. Drasco, Towards adiabatic waveforms for inspiral into Kerr black holes: II. Dynamical sources and generic orbits, Phys. Rev. D 78, 024022 (2008).
  122. S. Isoyama, R. Fujita, A. J. K. Chua, H. Nakano, A. Pound, and N. Sago, Adiabatic waveforms from extreme-mass-ratio inspirals: An analytical approach, Phys. Rev. Lett. 128, 231101 (2022).
  123. M. Kerachian, L. Polcar, V. Skoupý, C. Efthymiopoulos, and G. Lukes-Gerakopoulos, Action-angle formalism for extreme mass ratio inspirals in Kerr spacetime, Phys. Rev. D 108, 044004 (2023).
  124. Z. Nasipak, Adiabatic gravitational waveform model for compact objects undergoing quasicircular inspirals into rotating massive black holes, Phys. Rev. D 109, 044020 (2024).
  125. T. Nakamura, K. Oohara, and Y. Kojima, General relativistic collapse to black holes and gravitational waves from black holes, Prog. Theor. Phys. Suppl. 90, 1 (1987).
  126. M. Shibata, Gravitational waves induced by a particle orbiting around a rotating black hole: Spin orbit interaction effect, Phys. Rev. D 48, 663 (1993).
  127. M. Shibata, Gravitational waves induced by a particle orbiting around a rotating black hole: Effect of orbital precession, Prog. Theor. Phys. 90, 595 (1993).
  128. M. Shibata, Gravitational waves by compact stars orbiting around rotating supermassive black holes, Phys. Rev. D 50, 6297 (1994).
  129. D. Kennefick, Stability under radiation reaction of circular equatorial orbits around Kerr black holes, Phys. Rev. D 58, 064012 (1998).
  130. S. A. Hughes, The evolution of circular, nonequatorial orbits of Kerr black holes due to gravitational wave emission, Phys. Rev. D 61, 084004 (2000); 63, 049902(E) (2001); 65, 069902(E) (2002); 67, 089901(E) (2003); 78, 109902(E) (2008); 90, 109904(E) (2014).
  131. K. Glampedakis and D. Kennefick, Zoom and whirl: Eccentric equatorial orbits around spinning black holes and their evolution under gravitational radiation reaction, Phys. Rev. D 66, 044002 (2002).
  132. S. A. Hughes, S. Drasco, E. E. Flanagan, and J. Franklin, Gravitational radiation reaction and inspiral waveforms in the adiabatic limit, Phys. Rev. Lett. 94, 221101 (2005).
  133. Y. Mino, Self-force in the radiation reaction formula, Prog. Theor. Phys. 113, 733 (2005).
  134. R. Fujita, W. Hikida, and H. Tagoshi, An efficient numerical method for computing gravitational waves induced by a particle moving on eccentric inclined orbits around a Kerr black hole, Prog. Theor. Phys. 121, 843 (2009).
  135. E. Harms, S. Bernuzzi, A. Nagar, and A. Zenginoglu, A new gravitational wave generation algorithm for particle perturbations of the Kerr spacetime, Classical Quantum Gravity 31, 245004 (2014).
  136. R. Fujita and M. Shibata, Extreme mass ratio inspirals on the equatorial plane in the adiabatic order, Phys. Rev. D 102, 064005 (2020).
  137. C. Chen and J. Jing, Gravitational wave fluxes on generic orbits in near-extreme Kerr spacetime: Higher spin and large eccentricity, Sci. China Phys. Mech. Astron. 67, 110411 (2024).
  138. Y. Mino, M. Sasaki, M. Shibata, H. Tagoshi, and T. Tanaka, Black hole perturbation: Chapter 1, Prog. Theor. Phys. Suppl. 128, 1 (1997).
  139. M. Sasaki and H. Tagoshi, Analytic black hole perturbation approach to gravitational radiation, Living Rev. Relativity 6, 6 (2003).
  140. K. Ganz, W. Hikida, H. Nakano, N. Sago, and T. Tanaka, Adiabatic evolution of three ‘constants’ of motion for greatly inclined orbits in Kerr spacetime, Prog. Theor. Phys. 117, 1041 (2007).
  141. R. Fujita, Gravitational waves from a particle in circular orbits around a Schwarzschild black hole to the 22nd post-Newtonian order, Prog. Theor. Phys. 128, 971 (2012).
  142. A. G. Shah, Gravitational-wave flux for a particle orbiting a Kerr black hole to 20th post-Newtonian order: A numerical approach, Phys. Rev. D 90, 044025 (2014).
  143. R. Fujita, Gravitational waves from a particle in circular orbits around a rotating black hole to the 11th post-Newtonian order, Prog. Theor. Exp. Phys. 2015, 33E01 (2015).
  144. C. Munna, Analytic post-Newtonian expansion of the energy and angular momentum radiated to infinity by eccentric-orbit nonspinning extreme-mass-ratio inspirals to the 19th order, Phys. Rev. D 102, 124001 (2020).
  145. C. Munna and C. R. Evans, Eccentric-orbit extreme-mass-ratio-inspiral radiation II: 1PN correction to leading-logarithm and subleading-logarithm flux sequences and the entire perturbative 4PN flux, Phys. Rev. D 102, 104006 (2020).
  146. C. Munna, C. R. Evans, and E. Forseth, Tidal heating and torquing of the primary black hole in eccentric-orbit, nonspinning, extreme-mass-ratio inspirals to 22PN order, Phys. Rev. D 108, 044039 (2023).
  147. N. Sago, R. Fujita, and H. Nakano, Post-Newtonian templates for phase evolution of spherical extreme mass ratio inspirals, Phys. Rev. D 111, 064043 (2025).
  148. J. C. Castillo, C. R. Evans, C. Kavanagh, J. Neef, A. Ottewill, and B. Wardell, Post-Newtonian expansion of gravitational energy and angular momentum fluxes: Inclined spherical orbits about a Kerr black hole, Phys. Rev. D 111, 084004 (2025).
  149. O. Burke, G. A. Piovano, N. Warburton, P. Lynch, L. Speri, C. Kavanagh, B. Wardell, A. Pound, L. Durkan, and J. Miller, Assessing the importance of first postadiabatic terms for small-mass-ratio binaries, Phys. Rev. D 109, 124048 (2024).
  150. L. Barack and N. Sago, Gravitational self force on a particle in circular orbit around a Schwarzschild black hole, Phys. Rev. D 75, 064021 (2007).
  151. L. Barack and N. Sago, Gravitational self-force on a particle in eccentric orbit around a Schwarzschild black hole, Phys. Rev. D 81, 084021 (2010).
  152. T. Osburn, E. Forseth, C. R. Evans, and S. Hopper, Lorenz gauge gravitational self-force calculations of eccentric binaries using a frequency domain procedure, Phys. Rev. D 90, 104031 (2014).
  153. S. Isoyama, L. Barack, S. R. Dolan, A. Le Tiec, H. Nakano, A. G. Shah, T. Tanaka, and N. Warburton, Gravitational self-force correction to the innermost stable circular equatorial orbit of a Kerr black hole, Phys. Rev. Lett. 113, 161101 (2014).
  154. B. Wardell, Self-force: Computational strategies, Fund. Theor. Phys. 179, 487 (2015).
  155. M. van de Meent, Gravitational self-force on eccentric equatorial orbits around a Kerr black hole, Phys. Rev. D 94, 044034 (2016).
  156. M. van de Meent, Gravitational self-force on generic bound geodesics in Kerr spacetime, Phys. Rev. D 97, 104033 (2018).
  157. S. R. Dolan, L. Durkan, C. Kavanagh, and B. Wardell, Metric perturbations of Kerr spacetime in Lorenz gauge: Circular equatorial orbits, Classical Quantum Gravity 41, 155011 (2024).
  158. A. Pound, B. Wardell, N. Warburton, and J. Miller, Second-order self-force calculation of gravitational binding energy in compact binaries, Phys. Rev. Lett. 124, 021101 (2020).
  159. N. Warburton, A. Pound, B. Wardell, J. Miller, and L. Durkan, Gravitational-wave energy flux for compact binaries through second order in the mass ratio, Phys. Rev. Lett. 127, 151102 (2021).
  160. L. Durkan and N. Warburton, Slow evolution of the metric perturbation due to a quasicircular inspiral into a Schwarzschild black hole, Phys. Rev. D 106, 084023 (2022).
  161. L. V. Drummond, P. Lynch, A. G. Hanselman, D. R. Becker, and S. A. Hughes, Extreme mass-ratio inspiral and waveforms for a spinning body into a Kerr black hole via osculating geodesics and near-identity transformations, Phys. Rev. D 109, 064030 (2024).
  162. V. Skoupy, G. Lukes-Gerakopoulos, L. V. Drummond, and S. A. Hughes, Asymptotic gravitational-wave fluxes from a spinning test body on generic orbits around a Kerr black hole, Phys. Rev. D 108, 044041 (2023).
  163. G. A. Piovano, C. Pantelidou, J. Mac Uilliam, and V. Witzany, Spinning particles near Kerr black holes: Orbits and gravitational-wave fluxes through the Hamilton-Jacobi formalism, Phys. Rev. D 111, 044009 (2025).
  164. B. Wardell, A. Pound, N. Warburton, J. Miller, L. Durkan, and A. Le Tiec, Gravitational waveforms for compact binaries from second-order self-force theory, Phys. Rev. Lett. 130, 241402 (2023).
  165. M. Van De Meent and N. Warburton, Fast self-forced inspirals, Classical Quantum Gravity 35, 144003 (2018).
  166. P. Lynch, M. van de Meent, and N. Warburton, Eccentric self-forced inspirals into a rotating black hole, Classical Quantum Gravity 39, 145004 (2022).
  167. P. Lynch, Efficient trajectory calculations for extreme mass-ratio inspirals using near-identity (averaging) transformations, Ph.D. dissertation, University College Dublin, 2022, available electronically at http://hdl.handle.net/10197/13347.
  168. P. Lynch, M. van de Meent, and N. Warburton, Self-forced inspirals with spin-orbit precession, Phys. Rev. D 109, 084072 (2024).
  169. P. Lynch, V. Witzany, M. van de Meent, and N. Warburton, Fast inspirals and the treatment of orbital resonances, Classical Quantum Gravity 41, 225002 (2024).
  170. A. J. K. Chua, M. L. Katz, N. Warburton, and S. A. Hughes, Rapid generation of fully relativistic extreme-mass-ratio-inspiral waveform templates for LISA data analysis, Phys. Rev. Lett. 126, 051102 (2021).
  171. 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).
  172. C. Chapman-Bird, A. J. K. Chua, S. Hughes, M. Katz, Z. Nasipak, M. Pigou, L. Speri, and N. Warburton, Fastemriwaveforms, 10.5281/zenodo.15630565 (2025).
  173. 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 (2024).
  174. C. S. Reynolds, Observational constraints on black hole spin, Annu. Rev. Astron. Astrophys. 59, 117 (2021).
  175. O. Burke, J. R. Gair, J. Simón, and M. C. Edwards, Constraining the spin parameter of near-extremal black holes using LISA, Phys. Rev. D 102, 124054 (2020).
  176. K. S. Thorne, Disk accretion onto a black hole. 2. Evolution of the hole, Astrophys. J. 191, 507 (1974).
  177. J. M. Bardeen, Kerr metric black holes, Nature (London) 226, 64 (1970).
  178. A. Sadowski, M. Bursa, M. Abramowicz, W. Kluzniak, J.-P. Lasota, R. Moderski, and M. Safarzadeh, Spinning up black holes with super-critical accretion flows, Astron. Astrophys. 532, A41 (2011).
  179. A. Arbey, J. Auffinger, and J. Silk, Evolution of primordial black hole spin due to Hawking radiation, Mon. Not. R. Astron. Soc. 494, 1257 (2020).
  180. S. E. Gralla, S. A. Hughes, and N. Warburton, Inspiral into Gargantua, Classical Quantum Gravity 33, 155002 (2016); 37, 109501(E) (2020).
  181. G. Compère, K. Fransen, T. Hertog, and J. Long, Gravitational waves from plunges into Gargantua, Classical Quantum Gravity 35, 104002 (2018).
  182. O. Burke, J. R. Gair, and J. Simón, Transition from inspiral to plunge: A complete near-extremal trajectory and associated waveform, Phys. Rev. D 101, 064026 (2020).
  183. P. S. Cole, J. Alvey, L. Speri, C. Weniger, U. Bhardwaj, D. Gerosa, and G. Bertone, Sequential simulation-based inference for extreme mass ratio inspirals, arXiv:2505.16795.
  184. S. H. Strub, L. Speri, and D. Giardini, Searching for extreme mass ratio inspirals in LISA: From identification to parameter estimation, arXiv:2505.17814.
  185. C.-Q. Ye, H.-M. Fan, A. Torres-Orjuela, J.-d. Zhang, and Y.-M. Hu, Identification of gravitational waves from extreme-mass-ratio inspirals, Phys. Rev. D 109, 124034 (2024).
  186. A. J. K. Chua, One-stop function for gravitational-wave detection, identification, and inference, Phys. Rev. D 106, 104051 (2022).
  187. C. Badger, J. A. Font, M. Sakellariadou, and A. Torres-Forné, High-speed reconstruction of long-duration gravitational waves from extreme-mass-ratio inspirals using sparse dictionary learning, Phys. Rev. D 110, 064074 (2024).
  188. X.-T. Zhang, C. Messenger, N. Korsakova, M. L. Chan, Y.-M. Hu, and J.-d. Zhang, Detecting gravitational waves from extreme mass ratio inspirals using convolutional neural networks, Phys. Rev. D 105, 123027 (2022).
  189. Q. Yun, W.-B. Han, Y.-Y. Guo, H. Wang, and M. Du, The detection, extraction and parameter estimation of extreme-mass-ratio inspirals with deep learning, Sci. China Phys. Mech. Astron. 68, 210413 (2025).
  190. Q. Baghi, The LISA data challenges, in 56th Rencontres de Moriond on Gravitation (2022).
  191. L. V. Drummond, A. G. Hanselman, D. R. Becker, and S. A. Hughes, Extreme mass-ratio inspiral of a spinning body into a Kerr black hole I: Evolution along generic trajectories, arXiv:2305.08919.
  192. X. Feng, Z. Lyu, and H. Yang, Black-hole perturbation theory with post-Newtonian theory: Towards hybrid waveforms for neutron-star binaries, Phys. Rev. D 105, 104043 (2022).
  193. M. Rahman and A. Bhattacharyya, Prospects for determining the nature of the secondaries of extreme mass-ratio inspirals using the spin-induced quadrupole deformation, Phys. Rev. D 107, 024006 (2023).
  194. L. Xu, S. Yang, W. Han, X. Zhong, R. Tang, and Y. Zhang, Distinguishing compact objects in extreme-mass-ratio inspirals by gravitational waves, Universe 11, 18 (2025).
  195. L. Blanchet, Post-Newtonian theory for gravitational waves, Living Rev. Relativity 17, 2 (2014).
  196. L. Blanchet, G. Faye, Q. Henry, F. Larrouturou, and D. Trestini, Gravitational-wave phasing of quasicircular compact binary systems to the fourth-and-a-half post-Newtonian order, Phys. Rev. Lett. 131, 121402 (2023).
  197. L. Pompili et al., Laying the foundation of the effective-one-body waveform models SEOBNRv5: Improved accuracy and efficiency for spinning nonprecessing binary black holes, Phys. Rev. D 108, 124035 (2023).
  198. S. Albanesi, R. Gamba, S. Bernuzzi, J. Fontbuté, A. Gonzalez, and A. Nagar, Effective-one-body modeling for generic compact binaries with arbitrary orbits, arXiv:2503.14580.
  199. S. A. Hughes, Adiabatic and post-adiabatic approaches to extreme mass ratio inspiral, in 14th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics, and Relativistic Field Theories (2017), Vol. 2, pp. 1953–1959.
  200. P. Lynch and O. Burke, A note on the conversion of orbital angles for extreme mass ratio inspirals, arXiv:2411.04955.
  201. R. Fujita and W. Hikida, Analytical solutions of bound timelike geodesic orbits in Kerr spacetime, Classical Quantum Gravity 26, 135002 (2009).
  202. N. Warburton, B. Wardell, O. Long, S. Upton, P. Lynch, Z. Nasipak, and L. C. Stein, Kerrgeodesics, 10.5281/zenodo.8108265 (2023).
  203. S. Babak et al., LISA Rosetta Stone, LISA DDPC Convention Guide, 2025, internal DDPC document (to be published).
  204. E. E. Flanagan and T. Hinderer, Transient resonances in the inspirals of point particles into black holes, Phys. Rev. Lett. 109, 071102 (2012).
  205. M. van de Meent, Conditions for sustained orbital resonances in extreme mass ratio inspirals, Phys. Rev. D 89, 084033 (2014).
  206. C. P. L. Berry, R. H. Cole, P. Cañizares, and J. R. Gair, Importance of transient resonances in extreme-mass-ratio inspirals, Phys. Rev. D 94, 124042 (2016).
  207. M. van de Meent, Resonantly enhanced kicks from equatorial small mass-ratio inspirals, Phys. Rev. D 90, 044027 (2014).
  208. L. C. Stein and N. Warburton, Location of the last stable orbit in Kerr spacetime, Phys. Rev. D 101, 064007 (2020).
  209. A. Ori and K. S. Thorne, The transition from inspiral to plunge for a compact body in a circular equatorial orbit around a massive, spinning black hole, Phys. Rev. D 62, 124022 (2000).
  210. G. Compère and L. Küchler, Self-consistent adiabatic inspiral and transition motion, Phys. Rev. Lett. 126, 241106 (2021).
  211. G. Compère and Lorenzo Küchler, Asymptotically matched quasi-circular inspiral and transition-to-plunge in the small mass ratio expansion, SciPost Phys. 13, 043 (2022).
  212. S. A. Hughes, Parameterizing black hole orbits for adiabatic inspiral, Phys. Rev. D 109, 064077 (2024).
  213. T. Ng and E. Teo, Parametric solutions to the Kerr separatrix, Classical Quantum Gravity 42, 075003 (2025).
  214. G. Compère, Y. Liu, and J. Long, Classification of radial Kerr geodesic motion, Phys. Rev. D 105, 024075 (2022).
  215. S. A. Teukolsky, Perturbations of a rotating black hole. I. Fundamental equations for gravitational, electromagnetic, and neutrino-field perturbations, Astrophys. J. 185, 635 (1973).
  216. V. Skoupý and G. Lukes-Gerakopoulos, Spinning test body orbiting around a Kerr black hole: Eccentric equatorial orbits and their asymptotic gravitational-wave fluxes, Phys. Rev. D 103, 104045 (2021).
  217. Z. Nasipak, znasipak/pybhpt: v0.9.0, 10.5281/zenodo.15627818 (2025).
  218. M. van de Meent, Analytic solutions for parallel transport along generic bound geodesics in Kerr spacetime, Classical Quantum Gravity 37, 145007 (2020).
  219. C. Chapman-Bird, Z. Nasipak, and M. PIGOU, znasipak/multispline: v0.8.3, 10.5281/zenodo.15188413 (2025).
  220. G. Behforooz, End conditions for cubic spline interpolation derived from integration, Appl. Math. Comput. 29, 231 (1989).
  221. GSL—GNU Scientific Library, (https://www.gnu.org/software/gsl/) (1996).
  222. E. Hairer, S. Nørsett, and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems, ser. Springer Series in Computational Mathematics (Springer, Berlin, Heidelberg, 1993), pp. 192–193.
  223. B. Kocsis, N. Yunes, and A. Loeb, Observable signatures of EMRI black hole binaries embedded in thin accretion disks, Phys. Rev. D 84, 024032 (2011).
  224. M. Vallisneri, Use and abuse of the Fisher information matrix in the assessment of gravitational-wave parameter-estimation prospects, Phys. Rev. D 77, 042001 (2008).
  225. I. Gladwell, L. Shampine, and R. Brankin, Automatic selection of the initial step size for an ode solver, J. Comput. Appl. Math. 18, 175 (1987).
  226. R. Fujita (private communication).
  227. L. Lindblom, B. J. Owen, and D. A. Brown, Model waveform accuracy standards for gravitational wave data analysis, Phys. Rev. D 78, 124020 (2008).
  228. 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).
  229. R. Fujita and H. Tagoshi, New numerical methods to evaluate homogeneous solutions of the Teukolsky equation, Prog. Theor. Phys. 112, 415 (2004).
  230. R. Fujita and H. Tagoshi, New numerical methods to evaluate homogeneous solutions of the Teukolsky equation II. Solutions of the continued fraction equation, Prog. Theor. Phys. 113, 1165 (2005).
  231. Black Hole Perturbation Club (BHPC), (https://sites.google.com/view/bhpc1996/home) (2003).
  232. W. T. Throwe, High precision calculation of generic extreme mass ratio inspirals, Cambridge, MA, May 2010. [Online]. Available: http://hdl.handle.net/1721.1/61270.
  233. S. O’Sullivan and S. A. Hughes, Strong-field tidal distortions of rotating black holes: Formalism and results for circular, equatorial orbits, Phys. Rev. D 90, 124039 (2014); 91, 109901(E) (2015).
  234. R. Pordes, D. Petravick, B. Kramer, D. Olson, M. Livny, A. Roy, P. Avery, K. Blackburn, T. Wenaus, F. Würthwein, I. Foster, R. Gardner, M. Wilde, A. Blatecky, J. McGee, and R. Quick, The open science grid, J. Phys. Conf. Ser. 78, 012057 (2007).
  235. H. Khalvati, P. Lynch, O. Burke, L. Speri, M. van de Meent, and Z. Nasipak, Systematic errors in fast relativistic waveforms for Extreme Mass Ratio Inspirals, arXiv:2509.08875.
  236. M. A. Miller, Accuracy requirements for the calculation of gravitational waveforms from coalescing compact binaries in numerical relativity, Phys. Rev. D 71, 104016 (2005).
  237. E. E. Flanagan and S. A. Hughes, Measuring gravitational waves from binary black hole coalescences: 2. The waves’ information and its extraction, with and without templates, Phys. Rev. D 57, 4566 (1998).
  238. C. Cutler and M. Vallisneri, LISA detections of massive black hole inspirals: Parameter extraction errors due to inaccurate template waveforms, Phys. Rev. D 76, 104018 (2007).
  239. K. Chatziioannou, J. A. Clark, A. Bauswein, M. Millhouse, T. B. Littenberg, and N. Cornish, Inferring the post-merger gravitational wave emission from binary neutron star coalescences, Phys. Rev. D 96, 124035 (2017).
  240. M. Pürrer and C.-J. Haster, Gravitational waveform accuracy requirements for future ground-based detectors, Phys. Rev. Res. 2, 023151 (2020).
  241. A. Toubiana and J. R. Gair, Indistinguishability criterion and estimating the presence of biases, arXiv:2401.06845.
  242. A. J. K. Chua, M. L. Katz, N. Warburton, and S. A. Hughes, Rapid generation of fully relativistic extreme-mass-ratio-inspiral waveform templates for LISA data analysis, Phys. Rev. Lett. 126, 051102 (2021).
  243. L. Barack and C. Cutler, LISA capture sources: Approximate waveforms, signal-to-noise ratios, and parameter estimation accuracy, Phys. Rev. D 69, 082005 (2004).
  244. S. Babak, H. Fang, J. R. Gair, K. Glampedakis, and S. A. Hughes, ’Kludge’ gravitational waveforms for a test-body orbiting a Kerr black hole, Phys. Rev. D 75, 024005 (2007); 77, 04990(E) (2008).
  245. A. J. K. Chua, C. J. Moore, and J. R. Gair, Augmented kludge waveforms for detecting extreme-mass-ratio inspirals, Phys. Rev. D 96, 044005 (2017).
  246. M. Bonetti and A. Sesana, Gravitational wave background from extreme mass ratio inspirals, Phys. Rev. D 102, 103023 (2020).
  247. M. Piarulli, R. Buscicchio, F. Pozzoli, O. Burke, M. Bonetti, and A. Sesana, Test for LISA foreground Gaussianity and stationarity: Extreme mass-ratio inspirals, Phys. Rev. D 111, 103047 (2025).
  248. F. Pozzoli, S. Babak, A. Sesana, M. Bonetti, and N. Karnesis, Computation of stochastic background from extreme-mass-ratio inspiral populations for LISA, Phys. Rev. D 108, 103039 (2023); 110, 049903(E) (2024).
  249. P. C. Peters and J. Mathews, Gravitational radiation from point masses in a Keplerian orbit, Phys. Rev. 131, 435 (1963).
  250. S. Kejriwal, L. Speri, and A. J. K. Chua, Impact of correlations on the modeling and inference of beyond vacuum–general relativistic effects in extreme-mass-ratio inspirals, Phys. Rev. D 110, 084060 (2024).
  251. H. Tagoshi, PostNewtonian expansion of gravitational waves from a particle in slightly eccentric orbit around a rotating black hole, Prog. Theor. Phys. 93, 307 (1995); 118, 577(E) (2007).
  252. R. Fujita and B. R. Iyer, Spherical harmonic modes of 5.5 post-Newtonian gravitational wave polarisations and associated factorised resummed waveforms for a particle in circular orbit around a Schwarzschild black hole, Phys. Rev. D 82, 044051 (2010).
  253. P. C. Mahalanobis, Reprint of: Mahalanobis, p.c. (1936) “on the generalised distance in statistics”, Sankhya A 80, 1 (2018).
  254. J. R. Gair, L. Barack, T. Creighton, C. Cutler, S. L. Larson, E. S. Phinney, and M. Vallisneri, Event rate estimates for LISA extreme mass ratio capture sources, Classical Quantum Gravity 21, S1595 (2004).
  255. A. J. K. Chua and C. J. Cutler, Nonlocal parameter degeneracy in the intrinsic space of gravitational-wave signals from extreme-mass-ratio inspirals, Phys. Rev. D 106, 124046 (2022).
  256. J. E. Greene, J. Strader, and L. C. Ho, Intermediate-mass black holes, Annu. Rev. Astron. Astrophys. 58, 257 (2020).
  257. M. Bonetti and A. Sesana, Gravitational wave background from extreme mass ratio inspirals, Phys. Rev. D 102, 103023 (2020).
  258. N. Aghanim et al., Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  259. O. Lahav and A. R. Liddle, The cosmological parameters, arXiv:2403.15526.
  260. C. E. Rasmussen and C. K. I. Williams, Gaussian Processes for Machine Learning (The MIT Press, Cambridge, MA, 2005), 10.7551/mitpress/3206.001.0001.
  261. F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, Scikit-learn: Machine learning in Python, J. Mach. Learn. Res. 12, 2825 (2011).
  262. B. Rom, I. Linial, K. Kaur, and R. Sari, Dynamics around supermassive black holes: Extreme-mass-ratio Inspirals as gravitational-wave sources, Astrophys. J. 977, 7 (2024).
  263. L. Broggi, E. Bortolas, M. Bonetti, A. Sesana, and M. Dotti, Extreme mass ratio inspirals and tidal disruption events in nuclear clusters—I. Time-dependent rates, Mon. Not. R. Astron. Soc. 514, 3270 (2022).
  264. Y.-P. Li, H. Yang, and Z. Pan, Extreme mass-ratio inspirals in active galactic nucleus disks: The role of circumsingle disks, Phys. Rev. D 111, 063074 (2025).
  265. T. F. M. Spieksma and E. Cannizzaro, In the grip of the disk: Dragging the companion through an AGN, arXiv:2504.08033.
  266. F. D. Ryan, Effect of gravitational radiation reaction on circular orbits around a spinning black hole, Phys. Rev. D 52, R3159 (1995).
  267. D. Kennefick and A. Ori, Radiation reaction induced evolution of circular orbits of particles around Kerr black holes, Phys. Rev. D 53, 4319 (1996).
  268. R. Fujita, S. Isoyama, A. Le Tiec, H. Nakano, N. Sago, and T. Tanaka, Hamiltonian formulation of the conservative self-force dynamics in the Kerr geometry, Classical Quantum Gravity 34, 134001 (2017).
  269. G. Huez, S. Bernuzzi, M. Breschi, and R. Gamba, Gravitational waves from eccentric binary neutron star mergers: Systematic biases induced by quasi-circular templates, arXiv:2504.18622.
  270. M. L. Katz, J.-B. Bayle, A. J. K. Chua, and M. Vallisneri, Assessing the data-analysis impact of LISA orbit approximations using a GPU-accelerated response model, Phys. Rev. D 106, 103001 (2022).
  271. N. Karnesis, M. L. Katz, N. Korsakova, J. R. Gair, and N. Stergioulas, Eryn: A multipurpose sampler for Bayesian inference, Mon. Not. R. Astron. Soc. 526, 4814 (2023).
  272. M. Katz, N. Karnesis, and N. Korsakova, mikekatz04/eryn: First full release, 10.5281/zenodo.7705496 (2023).
  273. D. Foreman-Mackey, D. W. Hogg, D. Lang, and J. Goodman, emcee: The MCMC Hammer, Astron Soc Pac. 125, 306 (2013).
  274. E. Barausse, The evolution of massive black holes and their spins in their galactic hosts, Mon. Not. R. Astron. Soc. 423, 2533 (2012).
  275. R. Gray et al., Joint cosmological and gravitational-wave population inference using dark sirens and galaxy catalogues, J. Cosmol. Astropart. Phys. 12 (2023) 023.
  276. B. F. Schutz, Determining the Hubble constant from gravitational wave observations, Nature (London) 323, 310 (1986).
  277. S. Yi, F. Iacovelli, S. Marsat, D. Wadekar, and E. Berti, Systematic biases from the exclusion of higher harmonics in parameter estimation on LISA binaries, arXiv:2502.12237.
  278. S. Marsat, J. G. Baker, and T. Dal Canton, Exploring the Bayesian parameter estimation of binary black holes with LISA, Phys. Rev. D 103, 083011 (2021).
  279. A. Toubiana, L. Pompili, A. Buonanno, J. R. Gair, and M. L. Katz, Measuring source properties and quasinormal mode frequencies of heavy massive black-hole binaries with LISA, Phys. Rev. D 109, 104019 (2024).
  280. D. C. Wilkins, Bound geodesics in the Kerr metric, Phys. Rev. D 5, 814 (1972).
  281. E. Teo, Spherical photon orbits around a Kerr black hole, Gen. Relativ. Gravit. 35, 1909 (2003).
  282. E. Teo, Spherical orbits around a Kerr black hole, Gen. Relativ. Gravit. 53, 10 (2021).
  283. Black Hole Perturbation Toolkit, https://bhptoolkit.org/ (2018).
  284. A. Le Tiec, A. H. Mroue, L. Barack, A. Buonanno, H. P. Pfeiffer, N. Sago, and A. Taracchini, Periastron advance in black hole binaries, Phys. Rev. Lett. 107, 141101 (2011).
  285. M. van de Meent and H. P. Pfeiffer, Intermediate mass-ratio black hole binaries: Applicability of small mass-ratio perturbation theory, Phys. Rev. Lett. 125, 181101 (2020).
  286. B. Leather, A. Buonanno, and M. van de Meent, Inspiral-merger-ringdown waveforms with gravitational self-force results within the effective-one-body formalism, arXiv:2505.11242.
  287. A. Taracchini, A. Buonanno, G. Khanna, and S. A. Hughes, Small mass plunging into a Kerr black hole: Anatomy of the inspiral-merger-ringdown waveforms, Phys. Rev. D 90, 084025 (2014).
  288. H. Lim, G. Khanna, A. Apte, and S. A. Hughes, Exciting black hole modes via misaligned coalescences: II. The mode content of late-time coalescence waveforms, Phys. Rev. D 100, 084032 (2019).
  289. U. Ruangsri and S. A. Hughes, Census of transient orbital resonances encountered during binary inspiral, Phys. Rev. D 89, 084036 (2014).
  290. J. Brink, M. Geyer, and T. Hinderer, Astrophysics of resonant orbits in the Kerr metric, Phys. Rev. D 91, 083001 (2015).
  291. E. Levati, A. Cárdenas-Avendaño, K. Destounis, and P. Pani, Cumulative effect of orbital resonances in extreme-mass-ratio inspirals, Phys. Rev. D 111, 104006 (2025).
  292. C. M. Hirata, Resonant recoil in extreme mass ratio binary black hole mergers, Phys. Rev. D 83, 104024 (2011).
  293. P. Gupta, B. Bonga, A. J. K. Chua, and T. Tanaka, Importance of tidal resonances in extreme-mass-ratio inspirals, Phys. Rev. D 104, 044056 (2021).
  294. P. Gupta, T. Kakehi, and T. Tanaka, Resonant jumps induced by stationary tidal perturbation: A two-for-one deal, Classical Quantum Gravity 39, 245005 (2022).
  295. T. A. Apostolatos, G. Lukes-Gerakopoulos, and G. Contopoulos, How to observe a non-Kerr spacetime using gravitational waves, Phys. Rev. Lett. 103, 111101 (2009).
  296. Z. Pan, H. Yang, L. Bernard, and B. Bonga, Resonant dynamics of extreme mass-ratio inspirals in a perturbed Kerr spacetime, Phys. Rev. D 108, 104026 (2023).
  297. L. Speri and J. R. Gair, Assessing the impact of transient orbital resonances, Phys. Rev. D 103, 124032 (2021).
  298. Y. Xu, M. Rosselló-Sastre, S. Tiwari, M. Ebersold, E. Z. Hamilton, C. García-Quirós, H. Estellés, and S. Husa, Enhancing gravitational wave parameter estimation with nonlinear memory: Breaking the distance-inclination degeneracy, Phys. Rev. D 109, 123034 (2024).
  299. M. Rosselló-Sastre, S. Husa, S. Bera, and Y. Xu, Impact of the (ℓ=2,m=0) spherical harmonic mode with memory on parameter estimation for ground-based detectors, arXiv:2506.05859.
  300. T. Islam, S. E. Field, G. Khanna, and N. Warburton, Survey of gravitational wave memory in intermediate mass ratio binaries, Phys. Rev. D 108, 024046 (2023).
  301. K. Cunningham, C. Kavanagh, A. Pound, D. Trestini, N. Warburton, and J. Neef, Gravitational memory: New results from post-Newtonian and self-force theory, arXiv:2410.23950.
  302. A. Elhashash and D. A. Nichols, Waveform models for the gravitational-wave memory effect: Extreme mass-ratio limit and final memory offset, Phys. Rev. D 111, 044052 (2025).
  303. A. Spiers, A. Pound, and J. Moxon, Second-order Teukolsky formalism in Kerr spacetime: Formulation and nonlinear source, Phys. Rev. D 108, 064002 (2023).
  304. B. Leather and N. Warburton, Applying the effective-source approach to frequency-domain self-force calculations for eccentric orbits, Phys. Rev. D 108, 084045 (2023).
  305. T. Osburn and N. Nishimura, New self-force method via elliptic partial differential equations for Kerr inspiral models, Phys. Rev. D 106, 044056 (2022).
  306. Y.-X. Wei, J.-d. Zhang, and J. Mei, Second-order self-force for eccentric extreme-mass ratio inspirals on schwarzschild spacetime, arXiv:2504.09640.
  307. E. Harms, G. Lukes-Gerakopoulos, S. Bernuzzi, and A. Nagar, Asymptotic gravitational wave fluxes from a spinning particle in circular equatorial orbits around a rotating black hole, Phys. Rev. D 93, 044015 (2016); 100, 129901(A) (2019).
  308. S. Akcay, S. R. Dolan, C. Kavanagh, J. Moxon, N. Warburton, and B. Wardell, Dissipation in extreme-mass ratio binaries with a spinning secondary, Phys. Rev. D 102, 064013 (2020).
  309. G. A. Piovano, A. Maselli, and P. Pani, Extreme mass ratio inspirals with spinning secondary: A detailed study of equatorial circular motion, Phys. Rev. D 102, 024041 (2020).
  310. J. Mathews, A. Pound, and B. Wardell, Self-force calculations with a spinning secondary, Phys. Rev. D 105, 084031 (2022).
  311. A. Albertini, A. Nagar, J. Mathews, and G. Lukes-Gerakopoulos, Comparing second-order gravitational self-force and effective-one-body waveforms from inspiralling, quasicircular black hole binaries with a nonspinning primary and a spinning secondary, Phys. Rev. D 110, 044034 (2024).
  312. C. Chapman-Bird (to be published).
  313. I. Sfiligoi, D. C. Bradley, B. Holzman, P. Mhashilkar, S. Padhi, and F. Wurthwein, The pilot way to grid resources using glideinwms, in 2009 WRI World Congress on Computer Science and Information Engineering (2009), Vol. 2, pp. 428–432.
  314. OSG, Ospool, 2006. [Online]. Available: https://osg-htc.org/services/open_science_pool.html.
  315. Open science data federation, 2015. [Online]. Available: https://osdf.osg-htc.org/.
  316. C. Chapman-Bird, L. Speri, Z. Nasipak, O. Burke, M. L. Katz, A. Santini, S. Kejriwal, P. Lynch, J. Mathews, H. Khalvati, J. Thompson, S. Isoyama, S. A. Hughes, N. Warburton, A. J. K. Chua, and M. Pigou, Data release for “efficient waveforms for asymmetric-mass eccentric equatorial inspirals into rapidly-spinning black holes”, 10.5281/zenodo.15631641 (2025).
  317. C. Chapman-Bird, A. J. Chua, S. A. Hughes, M. L. Katz, Z. Nasipak, and N. Warburton, Data for fast emri waveforms, 10.5281/zenodo.15624459 (2025).
  318. J. C. Bardwell, Improving adiabatic trajectories of eccentric-equatorial extreme mass ratio inspirals with spinning massive black hole, Ph.D. dissertation, San Diego State University, 2024, copyright—Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works; Last updated—2025-03-14. [Online]. Available: https://www.proquest.com/dissertations-theses/improving-adiabatic-trajectories-eccentric/docview/3152477607/se-2.
  319. L. Speri, N. Karnesis, A. I. Renzini, and J. R. Gair, A roadmap of gravitational wave data analysis, Nat. Astron. 6, 1356 (2022).
  320. F. Pozzoli, R. Buscicchio, A. Klein, V. Korol, A. Sesana, and F. Haardt, Cyclostationary signals in LISA: A practical application to Milky Way satellites, Phys. Rev. D 111, 063005 (2025).
  321. M. C. Digman and N. J. Cornish, LISA gravitational wave sources in a time-varying galactic stochastic background, Astrophys. J. 940, 10 (2022).
  322. P. Whittle, Curve and periodogram smoothing, J. R. Stat. Soc. Ser. B (Statistical Methodology) 19, 38 (1957).
  323. T. A. Prince, M. Tinto, S. L. Larson, and J. W. Armstrong, The LISA optimal sensitivity, Phys. Rev. D 66, 122002 (2002).
  324. S. Babak, M. Hewitson, and A. Petiteau, LISA sensitivity and SNR calculations, arXiv:2108.01167.
  325. N. Karnesis, S. Babak, M. Pieroni, N. Cornish, and T. Littenberg, Characterization of the stochastic signal originating from compact binary populations as measured by LISA, Phys. Rev. D 104, 043019 (2021).
  326. T. Robson, N. J. Cornish, and C. Liu, The construction and use of LISA sensitivity curves, Classical Quantum Gravity 36, 105011 (2019).
  327. S. Kejriwal, O. Burke, and C. Chapman-Bird, Stableemrifisher (sef), manuscript in preparation. [Online]. Available: https://github.com/perturber/StableEMRIFisher.
  328. N. Sago and R. Fujita, Calculation of radiation reaction effect on orbital parameters in Kerr spacetime, Prog. Theor. Exp. Phys. 2015, 073E03 (2015).
  329. D. Bini, T. Damour, and A. Geralico, High post-Newtonian order gravitational self-force analytical results for eccentric equatorial orbits around a Kerr black hole, Phys. Rev. D 93, 124058 (2016).
  330. D. Bini and A. Geralico, New gravitational self-force analytical results for eccentric equatorial orbits around a Kerr black hole: Redshift invariant, Phys. Rev. D 100, 104002 (2019).
  331. C. Munna, High-order post-Newtonian expansion of the generalized redshift invariant for eccentric-orbit, equatorial extreme-mass-ratio inspirals with a spinning primary, Phys. Rev. D 108, 084012 (2023).
  332. V. Skoupý and V. Witzany, Post-Newtonian expansions of extreme mass ratio inspirals of spinning bodies into Schwarzschild black holes, Phys. Rev. D 110, 084061 (2024).
  333. D. Trestini, Z. Nasipak, and A. Pound (private communication).

Outline

Information

Phys. Rev. D 112, 104023– Published 12 November, 2025
  • Received 12 June 2025
  • Accepted 26 September 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation