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

Relieving Scale Disparity in Binary Black Hole Simulations

Nikolas A. Wittek1, Leor Barack2, Harald P. Pfeiffer1, Adam Pound2, Nils Deppe3,4,5, Lawrence E. Kidder5, Alexandra Macedo6, Kyle C. Nelli7, William Throwe5 et al.

Nils L. Vu7

Phys. Rev. Lett. 134, 251402 – Published 27 June, 2025

DOI: https://doi.org/10.1103/kskl-8dcj

Abstract

Worldtube excision is a method of reducing computational burden in numerical relativity simulations of binary black holes in situations where there is a good analytical model of the geometry around (one or both of) the objects. Two such scenarios of relevance in gravitational-wave astronomy are (1) the case of mass-disparate systems, and (2) the early inspiral when the separation is still large. Here we illustrate the utility and flexibility of this technique with simulations of the fully self-consistent radiative evolution in the model problem of a scalar charge orbiting a Schwarzschild black hole under the effect of scalar-field radiation reaction. We explore a range of orbital configurations, including inspirals with large eccentricity (which we follow through to the final plunge and ringdown) and hyperbolic scattering.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (84)

  1. R. Abbott et al. (KAGRA, VIRGO, LIGO Scientific Collaborations), 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. B. P. Abbott et al. (KAGRA, LIGO Scientific, Virgo Collaborations), Prospects for observing and localizing gravitational-wave transients with Advanced LIGO, Advanced Virgo and KAGRA, Living Rev. Relativity 23, 3 (2020).
  3. A. Dhani, S. Völkel, A. Buonanno, H. Estelles, J. Gair, H. P. Pfeiffer, L. Pompili, and A. Toubiana, Systematic biases in estimating the properties of black holes due to inaccurate gravitational-wave models, arXiv:2404.05811.
  4. M. Pürrer and C.-J. Haster, Gravitational waveform accuracy requirements for future ground-based detectors, Phys. Rev. Res. 2, 023151 (2020).
  5. Q. Hu and J. Veitch, Assessing the model waveform accuracy of gravitational waves, Phys. Rev. D 106, 044042 (2022).
  6. Q. Hu and J. Veitch, Accumulating errors in tests of general relativity with gravitational waves: Overlapping signals and inaccurate waveforms, Astrophys. J. 945, 103 (2023).
  7. A. Jan, D. Ferguson, J. Lange, D. Shoemaker, and A. Zimmerman, Accuracy limitations of existing numerical relativity waveforms on the data analysis of current and future ground-based detectors, Phys. Rev. D 110, 024023 (2024).
  8. C. B. Owen, C.-J. Haster, S. Perkins, N. J. Cornish, and N. Yunes, Waveform accuracy and systematic uncertainties in current gravitational wave observations, Phys. Rev. D 108, 044018 (2023).
  9. V. Kapil, L. Reali, R. Cotesta, and E. Berti, Systematic bias from waveform modeling for binary black hole populations in next-generation gravitational wave detectors, Phys. Rev. D 109, 104043 (2024).
  10. N. Afshordi et al. (LISA Consortium Waveform Working Group), Waveform modelling for the laser interferometer space antenna, arXiv:2311.01300.
  11. 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).
  12. M. Dhesi, H. R. Rüter, A. Pound, L. Barack, and H. P. Pfeiffer, Worldtube excision method for intermediate-mass-ratio inspirals: Scalar-field toy model, Phys. Rev. D 104, 124002 (2021).
  13. 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).
  14. N. Rosato, J. Healy, and C. O. Lousto, Adapted gauge to small mass ratio binary black hole evolutions, Phys. Rev. D 103, 104068 (2021).
  15. U. Sperhake, V. Cardoso, C. D. Ott, E. Schnetter, and H. Witek, Extreme black hole simulations: Collisions of unequal mass black holes and the point particle limit, Phys. Rev. D 84, 084038 (2011).
  16. 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).
  17. L. Barack and A. Pound, Self-force and radiation reaction in general relativity, Rep. Prog. Phys. 82, 016904 (2019).
  18. A. Albertini, A. Nagar, A. Pound, N. Warburton, B. Wardell, L. Durkan, and J. Miller, Comparing second-order gravitational self-force, numerical relativity, and effective one body waveforms from inspiralling, quasicircular, and nonspinning black hole binaries, Phys. Rev. D 106, 084061 (2022).
  19. 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).
  20. J. Mathews, A. Pound, B. Warburton, and B. Wardell, Post-adiabatic self-force waveforms: Slowly spinning primary and precessing secondary (to be published).
  21. N. A. Wittek et al., Worldtube excision method for intermediate-mass-ratio inspirals: Scalar-field model in 3+1 dimensions, Phys. Rev. D 108, 024041 (2023).
  22. 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).
  23. N. Deppe, W. Throwe, L. E. Kidder, N. L. Vu, K. C. Nelli, C. Armaza, M. S. Bonilla, F. Hébert, Y. Kim, P. Kumar, G. Lovelace, A. Macedo, J. Moxon, E. O’Shea, H. P. Pfeiffer, M. A. Scheel, S. A. Teukolsky, N. A. Wittek et al., SpECTRE v2024.09.29 (2024) 10.5281/zenodo.13858965.
  24. T. Damour, Gravitational scattering, post-Minkowskian approximation and effective one-body theory, Phys. Rev. D 94, 104015 (2016).
  25. Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M. P. Solon, and M. Zeng, Scattering amplitudes and the conservative Hamiltonian for binary systems at third post-Minkowskian order, Phys. Rev. Lett. 122, 201603 (2019).
  26. G. Kälin and R. A. Porto, From boundary data to bound states, J. High Energy Phys. 01 (2020) 072.
  27. G. Kälin, Z. Liu, and R. A. Porto, Conservative dynamics of binary systems to third post-Minkowskian order from the effective field theory approach, Phys. Rev. Lett. 125, 261103 (2020).
  28. M. Khalil, A. Buonanno, J. Steinhoff, and J. Vines, Energetics and scattering of gravitational two-body systems at fourth post-Minkowskian order, Phys. Rev. D 106, 024042 (2022).
  29. P. Rettegno, G. Pratten, L. M. Thomas, P. Schmidt, and T. Damour, Strong-field scattering of two spinning black holes: Numerical relativity versus post-Minkowskian gravity, Phys. Rev. D 108, 124016 (2023).
  30. T. Adamo, R. Gonzo, and A. Ilderton, Gravitational bound waveforms from amplitudes, J. High Energy Phys. 05 (2024) 034.
  31. J. Fontbuté, T. Andrade, R. Luna, J. C. Bustillo, G. Morrás, S. Jaraba, J. García-Bellido, and G. L. Izquierdo, A numerical-relativity surrogate model for hyperbolic encounters of black holes: Challenges in parameter estimation, Phys. Rev. D 111, 044024 (2025).
  32. G. U. Jakobsen, G. Mogull, J. Plefka, B. Sauer, and Y. Xu, Conservative scattering of spinning black holes at fourth post-Minkowskian order, Phys. Rev. Lett. 131, 151401 (2023).
  33. L. Barack et al., Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model, Phys. Rev. D 108, 024025 (2023).
  34. R. Gonzo, J. Lewis, and A. Pound, The first law of binary black hole scattering, arXiv:2409.03437.
  35. M. Driesse, G. U. Jakobsen, G. Mogull, J. Plefka, B. Sauer, and J. Usovitsch, Conservative black hole scattering at fifth post-Minkowskian and first self-force order, Phys. Rev. Lett. 132, 241402 (2024).
  36. O. Long, C. Whittall, and L. Barack, Black hole scattering near the transition to plunge: Self-force and resummation of post-Minkowskian theory, Phys. Rev. D 110, 044039 (2024).
  37. 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).
  38. 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).
  39. 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).
  40. 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).
  41. 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).
  42. A. Pound and B. Wardell, Black hole perturbation theory and gravitational self-force, in Handbook of Gravitational Wave Astronomy, edited by C. Bambi, S. Katsanevas, and K. D. Kokkotas (Springer Nature Singapore, Singapore, 2022), pp. 1411–1529.
  43. J. McCart, T. Osburn, and J. Y. J. Burton, Highly eccentric extreme-mass-ratio-inspiral waveforms via fast self-forced inspirals, Phys. Rev. D 104, 084050 (2021).
  44. 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).
  45. Z. Nasipak, Adiabatic gravitational waveform model for compact objects undergoing quasicircular inspirals into rotating massive black holes, Phys. Rev. D 109, 044020 (2024).
  46. T. C. Quinn, Axiomatic approach to radiation reaction of scalar point particles in curved spacetime, Phys. Rev. D 62, 064029 (2000).
  47. E. Poisson, A. Pound, and I. Vega, The motion of point particles in curved spacetime, Living Rev. Relativity 14, 7 (2011).
  48. A. I. Harte, Motion in classical field theories and the foundations of the self-force problem, Fund. Theor. Phys. 179, 327 (2015).
  49. S. L. Detweiler and B. F. Whiting, Selfforce via a Green’s function decomposition, Phys. Rev. D 67, 024025 (2003).
  50. M. A. Scheel, H. P. Pfeiffer, L. Lindblom, L. E. Kidder, O. Rinne, and S. A. Teukolsky, Solving Einstein’s equations with dual coordinate frames, Phys. Rev. D 74, 104006 (2006).
  51. D. A. Hemberger, M. A. Scheel, L. E. Kidder, B. Szilágyi, G. Lovelace, N. W. Taylor, and S. A. Teukolsky, Dynamical excision boundaries in spectral evolutions of binary black hole spacetimes, Classical Quantum Gravity 30, 115001 (2013).
  52. M. A. Scheel, M. Giesler, D. A. Hemberger, G. Lovelace, K. Kuper, M. Boyle, B. Szilágyi, and L. E. Kidder, Improved methods for simulating nearly extremal binary black holes, Classical Quantum Gravity 32, 105009 (2015).
  53. G. Lovelace et al., Simulating binary black hole mergers using discontinuous Galerkin methods, Classical Quantum Gravity 42, 035001 (2025).
  54. See Supplemental Material at http://link.aps.org/supplemental/10.1103/kskl-8dcj for numerical convergence tests.
  55. M. Boyle et al., The SXS Collaboration catalog of binary black hole simulations, Classical Quantum Gravity 36, 195006 (2019).
  56. J. Moxon, M. A. Scheel, S. A. Teukolsky, N. Deppe, N. Vu, F. Hébert, L. E. Kidder, and W. Throwe, SpECTRE Cauchy-characteristic evolution system for rapid, precise waveform extraction, Phys. Rev. D 107, 064013 (2023).
  57. N. Warburton, S. Akcay, L. Barack, J. R. Gair, and N. Sago, Evolution of inspiral orbits around a Schwarzschild black hole, Phys. Rev. D 85, 061501(R) (2012).
  58. M. Van De Meent and N. Warburton, Fast self-forced inspirals, Classical Quantum Gravity 35, 144003 (2018).
  59. 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.
  60. L. Barack and O. Long, Self-force correction to the deflection angle in black-hole scattering: A scalar charge toy model, Phys. Rev. D 106, 104031 (2022).
  61. L. Küchler, G. Compère, L. Durkan, and A. Pound, Self-force framework for transition-to-plunge waveforms, SciPost Phys. 17, 056 (2024).
  62. D. R. Becker and S. A. Hughes, Transition from adiabatic inspiral to plunge for eccentric binaries, Phys. Rev. D 111, 064003 (2025).
  63. E. Poisson, Metric of a tidally distorted, nonrotating black hole, Phys. Rev. Lett. 94, 161103 (2005).
  64. E. Poisson and I. Vlasov, Geometry and dynamics of a tidally deformed black hole, Phys. Rev. D 81, 024029 (2010).
  65. E. Poisson and E. Corrigan, Nonrotating black hole in a post-Newtonian tidal environment II, Phys. Rev. D 97, 124048 (2018).
  66. N. Yunes and J. Gonzalez, Metric of a tidally perturbed spinning black hole, Phys. Rev. D 73, 024010 (2006); 89, 089902(E) (2014).
  67. K. Chatziioannou, E. Poisson, and N. Yunes, Improved next-to-leading order tidal heating and torquing of a Kerr black hole, Phys. Rev. D 94, 084043 (2016).
  68. P. Pani, L. Gualtieri, A. Maselli, and V. Ferrari, Tidal deformations of a spinning compact object, Phys. Rev. D 92, 024010 (2015).
  69. A. Le Tiec, M. Casals, and E. Franzin, Tidal love numbers of Kerr black holes, Phys. Rev. D 103, 084021 (2021).
  70. L. Kale et al., UIUC-PPL/charm: charm++ version 7.0.0 (2021).
  71. L. V. Kale and S. Krishnan, charm++: Parallel programming with message-driven objects, in Parallel Programming using c++, edited by G. V. Wilson and P. Lu (The MIT Press, Cambridge, MA, 1996), pp. 175–213.
  72. K. Iglberger, G. Hager, J. Treibig, and U. Rüde, High performance smart expression template math libraries, in Proceedings of the 2012 International Conference on High Performance Computing & Simulation (HPCS) (IEEE, New York, 2012), pp. 367–373.
  73. K. Iglberger, G. Hager, J. Treibig, and U. Rüde, Expression templates revisited: A performance analysis of current methodologies, SIAM J. Sci. Comput. 34, C42 (2012).
  74. The HDF Group, Hierarchical Data Format, version 5 (1997–2023), https://www.hdfgroup.org/HDF5/.
  75. M. Galassi et al., GNU Scientific Library Reference Manual, 3rd ed. (Network Theory Ltd., Surrey, United Kingdom, 2009).
  76. J. Beder et al., yaml-cpp (2009), 10.11578/dc.20220817.13.
  77. W. Jakob, J. Rhinelander, and D. Moldovan, pybind11: Seamless operability between c++11 and python (2017), https://github.com/pybind/pybind11.
  78. M. Reinecke and D. S. Seljebotn, Libsharp: Spherical harmonic transforms revisited, Astron. Astrophys. 554, A112 (2013).
  79. A. Heinecke, G. Henry, M. Hutchinson, and H. Pabst, LIBXSMM: Accelerating small matrix multiplications by runtime code generation, in Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, SC ’16 (IEEE Press, New York, 2016), pp. 1–11.
  80. J. D. Hunter, matplotlib: A 2d graphics environment, Comput. Sci. Eng. 9, 90 (2007).
  81. T. A. Caswell et al., matplotlib/matplotlib: REL: v3.3.0 (2020).
  82. C. R. Harris et al., Array programming with numpy, Nature (London) 585, 357 (2020).
  83. U. Ayachit, The ParaView Guide: A Parallel Visualization Application (Kitware, Inc., Clifton Park, NY, USA, 2015).
  84. J. Ahrens, B. Geveci, and C. Law, ParaView: An End-User Tool for Large-Data Visualization (Elsevier, New York, 2005).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation