- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

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
  • Access by Xinjiang University

Gravitational memory from hairy binary black hole mergers

Silvia Gasparotto1,*, Jann Zosso2,†, Llibert Aresté Saló3,4,‡, Daniela D. Doneva5,6,§, and Stoytcho S. Yazadjiev7,8,∥

  • *Contact author: silvia.gasparotto@cern.ch
  • †Contact author: jann.zosso@nbi.ku.dk
  • ‡Contact author: llibert.arestesalo@kuleuven.be
  • §Contact author: daniela.doneva@uv.es
  • ∥Contact author: yazad@phys.uni-sofia.bg
PDF

Phys. Rev. D 114, 044094 – Published 26 August, 2026

DOI: https://doi.org/10.1103/6sry-t38l

Abstract

Gravitational-wave memory is a low-frequency, nonoscillatory component of the radiation field that provides a potentially powerful but as yet undetected probe of strong-field gravity. We present the first calculation of gravitational memory from full inspiral-merger-ringdown waveforms in a theory beyond general relativity, focusing on scalar-Gauss-Bonnet gravity as a theoretically well-motivated and numerically accessible extension of GR. Starting from the general memory formulas in Horndeski gravity, we derive explicit spin-weighted spherical-harmonic expressions for the tensor null memory in scalar-Gauss-Bonnet theory and evaluate them on existing numerical-relativity waveforms for both shift-symmetric and dynamically scalarizing binary black hole mergers. We find that the dominant effect is an indirect modification of the tensor memory through changes in the nonlinear merger dynamics, while the direct scalar contribution to the tensor memory remains suppressed by orders of magnitude for the systems considered in this work. For the largest deviations in our dataset, the final memory amplitude differs from the corresponding GR prediction by a few percent and by up to ∼4% when compared to the GR template that minimizes the waveform mismatch in a detector-oriented analysis. We further show that including memory increases the mismatch between GR and scalar-Gauss-Bonnet waveforms by more than an order of magnitude, indicating that memory can provide complementary information for testing gravity with third-generation detectors, especially for low-mass binaries.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (163)

  1. A. G. Abac et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), GWTC-4.0: Updating the gravitational-wave transient catalog with observations from the first part of the fourth LIGO-Virgo-KAGRA observing run, Astrophys. J. Lett. 1004, L22 (2026).
  2. A. G. Abac et al. (LIGO Scientific, KAGRA, and Virgo Collaborations), GWTC-4.0: An introduction to version 4.0 of the gravitational-wave transient catalog, Astrophys. J. Lett. 995, L18 (2025).
  3. A. G. Abac et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), GWTC-4.0: Methods for identifying and characterizing gravitational-wave transients, Astrophys. J. Lett. 1004, L21 (2026).
  4. G. Agazie et al. (NANOGrav Collaboration), The NANOGrav 15 yr data set: Evidence for a gravitational-wave background, Astrophys. J. Lett. 951, L8 (2023).
  5. D. J. Reardon et al., Search for an isotropic gravitational-wave background with the Parkes Pulsar Timing Array, Astrophys. J. Lett. 951, L6 (2023).
  6. J. Antoniadis et al. (EPTA, InPTA Collaborations), The second data release from the European Pulsar Timing Array—III. Search for gravitational wave signals, Astron. Astrophys. 678, A50 (2023).
  7. A. Abac et al. (ET Collaboration), The science of the Einstein telescope, J. Cosmol. Astropart. Phys. 03 (2026) 081.
  8. D. Reitze et al., Cosmic explorer: The U.S. Contribution to gravitational-wave astronomy beyond LIGO, Bull. Am. Astron. Soc. 51, 035 (2019).
  9. M. Colpi et al. (LISA Collaboration), LISA definition study report, arXiv:2402.07571.
  10. J. Mei et al. (TianQin Collaboration), The TianQin project: Current progress on science and technology, Prog. Theor. Exp. Phys. 2021, 05A107 (2021).
  11. Y. B. Zel’dovich and A. G. Polnarev, Radiation of gravitational waves by a cluster of superdense stars, Sov. Astron. 18, 17 (1974), https://ui.adsabs.harvard.edu/scan/manifest/1974SvA....18...17Z.
  12. V. B. Braginsky and L. P. Grishchuk, Kinematic resonance and memory effect in free mass gravitational antennas, Sov. Phys. JETP 62, 427 (1985), https://inspirehep.net/literature/237866.
  13. V. B. Braginsky and K. S. Thorne, Gravitational-wave bursts with memory and experimental prospects, Nature (London) 327, 123 (1987).
  14. K. S. Thorne, Gravitational-wave bursts with memory: The Christodoulou effect, Phys. Rev. D 45, 520 (1992).
  15. D. Christodoulou, Nonlinear nature of gravitation and gravitational wave experiments, Phys. Rev. Lett. 67, 1486 (1991).
  16. L. Blanchet and T. Damour, Hereditary effects in gravitational radiation, Phys. Rev. D 46, 4304 (1992).
  17. A. G. Wiseman and C. M. Will, Christodoulou’s nonlinear gravitational wave memory: Evaluation in the quadrupole approximation, Phys. Rev. D 44, R2945 (1991).
  18. M. Favata, Nonlinear gravitational-wave memory from binary black hole mergers, Astrophys. J. Lett. 696, L159 (2009).
  19. H. Bondi, M. G. J. van der Burg, and A. W. K. Metzner, Gravitational waves in general relativity. 7. Waves from axisymmetric isolated systems, Proc. R. Soc. A 269, 21 (1962).
  20. R. K. Sachs, Gravitational waves in general relativity. 8. Waves in asymptotically flat space-times, Proc. R. Soc. A 270, 103 (1962).
  21. S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140, B516 (1965).
  22. A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory (Princeton University Press, Princeton, NJ, 2018).
  23. A. Strominger, On BMS invariance of gravitational scattering, J. High Energy Phys. 07 (2014) 152.
  24. T. He, V. Lysov, P. Mitra, and A. Strominger, BMS supertranslations and Weinberg’s soft graviton theorem, J. High Energy Phys. 05 (2015) 151.
  25. A. Strominger and A. Zhiboedov, Gravitational memory, BMS supertranslations and soft theorems, J. High Energy Phys. 01 (2016) 086.
  26. S. Pasterski, A. Strominger, and A. Zhiboedov, New gravitational memories, J. High Energy Phys. 12 (2016) 053.
  27. É. É. Flanagan, A. M. Grant, A. I. Harte, and D. A. Nichols, Persistent gravitational wave observables: General framework, Phys. Rev. D 99, 084044 (2019).
  28. A. M. Grant and D. A. Nichols, Persistent gravitational wave observables: Curve deviation in asymptotically flat spacetimes, Phys. Rev. D 105, 024056 (2022); 107, 109902(E) (2023).
  29. M. Hübner, C. Talbot, P. D. Lasky, and E. Thrane, Measuring gravitational-wave memory in the first LIGO/Virgo gravitational-wave transient catalog, Phys. Rev. D 101, 023011 (2020).
  30. M. Hübner, P. Lasky, and E. Thrane, Memory remains undetected: Updates from the second LIGO/Virgo gravitational-wave transient catalog, Phys. Rev. D 104, 023004 (2021).
  31. A. M. Grant and D. A. Nichols, Outlook for detecting the gravitational-wave displacement and spin memory effects with current and future gravitational-wave detectors, Phys. Rev. D 107, 064056 (2023); 108, 029901(E) (2023).
  32. S. Gasparotto, R. Vicente, D. Blas, A. C. Jenkins, and E. Barausse, Can gravitational-wave memory help constrain binary black-hole parameters? A LISA case study, Phys. Rev. D 107, 124033 (2023).
  33. H. Inchauspé, S. Gasparotto, D. Blas, L. Heisenberg, J. Zosso, and S. Tiwari, Measuring gravitational wave memory with LISA, Phys. Rev. D 111, 044044 (2025).
  34. A. Cogez, S. Gasparotto, J. Zosso, H. Inchauspé, C. Pitte, L. Magaña Zertuche, A. Petiteau, and M. Besancon, Detectability of gravitational-wave memory with LISA: A Bayesian approach, Phys. Rev. D 113, 104034 (2026).
  35. J. Zosso, L. Magaña Zertuche, S. Gasparotto, A. Cogez, H. Inchauspé, and M. Jacobs, Toward claiming a detection of gravitational memory, Phys. Rev. D 113, 104033 (2026).
  36. S. M. Tomson et al., Search for gravitational-wave memory in PPTA and EPTA data: A complete signal model, Astrophys. J. Lett. 996, L9 (2026).
  37. S. Hou, Z.-C. Zhao, Z. Cao, and Z.-H. Zhu, Space-Borne interferometers to detect thousands of memory signals emitted by stellar-mass binary black holes, Chin. Phys. Lett. 42, 101101 (2025).
  38. S. Gasparotto, G. Franciolini, and V. Domcke, Gravitational wave memory of primordial black hole mergers, Phys. Rev. D 112, 103021 (2025).
  39. S. Ghosh, A. Weaver, J. Sanjuan, P. Fulda, and G. Mueller, Detection of the gravitational memory effect in LISA using triggers from ground-based detectors, Phys. Rev. D 107, 084051 (2023).
  40. L. Heisenberg, N. Yunes, and J. Zosso, Gravitational wave memory beyond general relativity, Phys. Rev. D 108, 024010 (2023).
  41. L. Heisenberg, G. Xu, and J. Zosso, Unifying ordinary and null memory, J. Cosmol. Astropart. Phys. 05 (2024) 119.
  42. J. Zosso, Continuing Isaacson’s legacy: A general metric theory perspective on gravitational memory and the non-linearity of gravity, in 59th Rencontres de Moriond on Gravitation: Moriond 2025 Gravitation (2025), p. 5; arXiv:2505.17603.
  43. G. W. Horndeski, Second-order scalar-tensor field equations in a four-dimensional space, Int. J. Theor. Phys. 10, 363 (1974).
  44. A. Nicolis, R. Rattazzi, and E. Trincherini, The Galileon as a local modification of gravity, Phys. Rev. D 79, 064036 (2009).
  45. C. Deffayet, G. Esposito-Farese, and A. Vikman, Covariant Galileon, Phys. Rev. D 79, 084003 (2009).
  46. C. Deffayet, S. Deser, and G. Esposito-Farese, Generalized Galileons: All scalar models whose curved background extensions maintain second-order field equations and stress-tensors, Phys. Rev. D 80, 064015 (2009).
  47. L. Heisenberg, A systematic approach to generalisations of general relativity and their cosmological implications, Phys. Rep. 796, 1 (2019).
  48. T. Kobayashi, Horndeski theory and beyond: A review, Rep. Prog. Phys. 82, 086901 (2019).
  49. M. Fierz, On the physical interpretation of P. Jordan’s extended theory of gravitation, Helv. Phys. Acta 29, 128 (1956), https://inspirehep.net/literature/48322.
  50. C. Brans and R. H. Dicke, Mach’s principle and a relativistic theory of gravitation, Phys. Rev. 124, 925 (1961).
  51. B. Zwiebach, Curvature squared terms and string theories, Phys. Lett. 156B, 315 (1985).
  52. D. J. Gross and E. Witten, Superstring modifications of Einstein’s equations, Nucl. Phys. B277, 1 (1986).
  53. D. G. Boulware and S. Deser, Effective gravity theories with dilatons, Phys. Lett. B 175, 409 (1986).
  54. F. Moura and R. Schiappa, Higher-derivative corrected black holes: Perturbative stability and absorption cross-section in heterotic string theory, Classical Quantum Gravity 24, 361 (2007).
  55. S. Nojiri, S. D. Odintsov, and M. Sasaki, Gauss-Bonnet dark energy, Phys. Rev. D 71, 123509 (2005).
  56. S. Nojiri, S. D. Odintsov, and M. Sami, Dark energy cosmology from higher-order, string-inspired gravity and its reconstruction, Phys. Rev. D 74, 046004 (2006).
  57. P. Pani and V. Cardoso, Are black holes in alternative theories serious astrophysical candidates? the case for Einstein-Dilaton-Gauss-Bonnet black holes, Phys. Rev. D 79, 084031 (2009).
  58. P. Pani, E. Berti, V. Cardoso, and J. Read, Compact stars in alternative theories of gravity. Einstein-Dilaton-Gauss-Bonnet gravity, Phys. Rev. D 84, 104035 (2011).
  59. S. Tahura, D. A. Nichols, A. Saffer, L. C. Stein, and K. Yagi, Brans-Dicke theory in Bondi-Sachs form: Asymptotically flat solutions, asymptotic symmetries and gravitational-wave memory effects, Phys. Rev. D 103, 104026 (2021).
  60. S. Tahura, D. A. Nichols, and K. Yagi, Gravitational-wave memory effects in Brans-Dicke theory: Waveforms and effects in the post-Newtonian approximation, Phys. Rev. D 104, 104010 (2021).
  61. S. Hou and Z.-H. Zhu, Gravitational memory effects and Bondi-Metzner-Sachs symmetries in scalar-tensor theories, J. High Energy Phys. 01 (2021) 083.
  62. S. Hou and Z.-H. Zhu, “Conserved charges” of the Bondi-Metzner-Sachs algebra in the Brans-Dicke theory, Chin. Phys. C 45, 023122 (2021).
  63. S. Tahura, D. A. Nichols, and K. Yagi, Gravitational-wave memory effects in the Damour-Esposito-Farèse extension of Brans-Dicke theory, Phys. Rev. D 112, 084037 (2025).
  64. S. M. Du and A. Nishizawa, Gravitational wave memory: A new approach to study modified gravity, Phys. Rev. D 94, 104063 (2016).
  65. K. Koyama, Testing Brans-Dicke gravity with screening by scalar gravitational wave memory, Phys. Rev. D 102, 021502 (2020).
  66. D. Maibach and J. Zosso, Balance flux laws beyond general relativity, Phys. Rev. D 113, 124085 (2026).
  67. S. Hou, T. Zhu, and Z.-H. Zhu, Asymptotic analysis of Chern-Simons modified gravity and its memory effects, Phys. Rev. D 105, 024025 (2022).
  68. S. Hou, T. Zhu, and Z.-H. Zhu, Conserved charges in Chern-Simons modified theory and memory effects, J. Cosmol. Astropart. Phys. 04 (2022) 032.
  69. L. Heisenberg, B. Rosatello, G. Xu, and J. Zosso, Constraining superluminal Einstein-Æther gravity through gravitational memory, Phys. Rev. D 112, 024052 (2025).
  70. L. Heisenberg, B. Rosatello, G. Xu, and J. Zosso, Gravitational memory in generalized Proca gravity, Phys. Rev. D 112, 104073 (2025).
  71. R. N. Lang, Compact binary systems in scalar-tensor gravity. II. Tensor gravitational waves to second post-Newtonian order, Phys. Rev. D 89, 084014 (2014).
  72. N. Sennett, S. Marsat, and A. Buonanno, Gravitational waveforms in scalar-tensor gravity at 2PN relative order, Phys. Rev. D 94, 084003 (2016).
  73. L. Bernard, L. Blanchet, and D. Trestini, Gravitational waves in scalar-tensor theory to one-and-a-half post-Newtonian order, J. Cosmol. Astropart. Phys. 08 (2022) 008.
  74. D. Trestini, Quasi-Keplerian parametrization for eccentric compact binaries in scalar-tensor theories at second post-Newtonian order and applications, Phys. Rev. D 109, 104003 (2024).
  75. P. C. C. Freire and N. Wex, Gravity experiments with radio pulsars, Living Rev. Relativity 27, 5 (2024).
  76. J. Z. Simon, Higher-derivative Lagrangians, nonlocality, problems, and solutions, Phys. Rev. D 41, 3720 (1990).
  77. N. Yunes and X. Siemens, Gravitational-wave tests of general relativity with Ground-Based detectors and pulsar Timing-Arrays, Living Rev. Relativity 16, 9 (2013).
  78. J. Zosso, Probing gravity—fundamental aspects of metric theories and their implications for tests of general relativity, Ph.D. thesis, Zurich, ETH, 2024, arXiv:2412.06043.
  79. S. Weinberg, Effective field theory for inflation, Phys. Rev. D 77, 123541 (2008).
  80. R. R. Metsaev and A. A. Tseytlin, Order alpha-prime (two loop) equivalence of the string equations of motion and the sigma model Weyl invariance conditions: Dependence on the dilaton and the antisymmetric tensor, Nucl. Phys. B293, 385 (1987).
  81. T. Torii, H. Yajima, and K.-i. Maeda, Dilatonic black holes with Gauss-Bonnet term, Phys. Rev. D 55, 739 (1997).
  82. S. Nojiri, S. D. Odintsov, and V. K. Oikonomou, Modified gravity theories on a nutshell: Inflation, bounce and late-time evolution, Phys. Rep. 692, 1 (2017).
  83. A. Ortega, T. Daniel, and S. M. Koushiappas, Field equations in Chern-Simons-Gauss-Bonnet gravity, Phys. Rev. D 111, 063506 (2025).
  84. M. Ostrogradsky, Mémoires sur les équations différentielles, relatives au problème des isopérimètres, Mem. Acad. St. Petersbourg 6, 385 (1850).
  85. R. P. Woodard, Ostrogradsky’s theorem on Hamiltonian instability, Scholarpedia 10, 32243 (2015).
  86. C. de Rham and A. Matas, Ostrogradsky in theories with multiple fields, J. Cosmol. Astropart. Phys. 06 (2016) 041.
  87. Á. D. Kovács and H. S. Reall, Well-posed formulation of Lovelock and Horndeski theories, Phys. Rev. D 101, 124003 (2020).
  88. Á. D. Kovács and H. S. Reall, Well-posed formulation of scalar-tensor effective field theory, Phys. Rev. Lett. 124, 221101 (2020).
  89. P. Kanti, N. E. Mavromatos, J. Rizos, K. Tamvakis, and E. Winstanley, Dilatonic black holes in higher curvature string gravity, Phys. Rev. D 54, 5049 (1996).
  90. B. Kleihaus, J. Kunz, and E. Radu, Rotating black holes in dilatonic Einstein-Gauss-Bonnet theory, Phys. Rev. Lett. 106, 151104 (2011).
  91. T. P. Sotiriou and S.-Y. Zhou, Black hole hair in generalized scalar-tensor gravity, Phys. Rev. Lett. 112, 251102 (2014).
  92. D. D. Doneva and S. S. Yazadjiev, New Gauss-Bonnet black holes with curvature-Induced scalarization in extended scalar-tensor theories, Phys. Rev. Lett. 120, 131103 (2018).
  93. H. O. Silva, J. Sakstein, L. Gualtieri, T. P. Sotiriou, and E. Berti, Spontaneous scalarization of black holes and compact stars from a Gauss-Bonnet coupling, Phys. Rev. Lett. 120, 131104 (2018).
  94. G. Antoniou, A. Bakopoulos, and P. Kanti, Evasion of No-Hair theorems and novel black-hole solutions in Gauss-Bonnet theories, Phys. Rev. Lett. 120, 131102 (2018).
  95. P. V. P. Cunha, C. A. R. Herdeiro, and E. Radu, Spontaneously scalarized Kerr black holes in extended scalar-tensor–Gauss-Bonnet gravity, Phys. Rev. Lett. 123, 011101 (2019).
  96. L. G. Collodel, B. Kleihaus, J. Kunz, and E. Berti, Spinning and excited black holes in Einstein-scalar-Gauss–Bonnet theory, Classical Quantum Gravity 37, 075018 (2020).
  97. E. Berti, L. G. Collodel, B. Kleihaus, and J. Kunz, Spin-induced black-hole scalarization in Einstein-scalar-Gauss-Bonnet theory, Phys. Rev. Lett. 126, 011104 (2021).
  98. C. A. R. Herdeiro, E. Radu, H. O. Silva, T. P. Sotiriou, and N. Yunes, Spin-induced scalarized black holes, Phys. Rev. Lett. 126, 011103 (2021).
  99. W. E. East and J. L. Ripley, Evolution of Einstein-scalar-Gauss-Bonnet gravity using a modified harmonic formulation, Phys. Rev. D 103, 044040 (2021).
  100. W. E. East and J. L. Ripley, Dynamics of spontaneous black hole scalarization and mergers in Einstein-Scalar-Gauss-Bonnet gravity, Phys. Rev. Lett. 127, 101102 (2021).
  101. L. Aresté Saló, K. Clough, and P. Figueras, Well-posedness of the four-derivative scalar-tensor theory of gravity in singularity avoiding coordinates, Phys. Rev. Lett. 129, 261104 (2022).
  102. L. Aresté Saló, K. Clough, and P. Figueras, Puncture gauge formulation for Einstein-Gauss-Bonnet gravity and four-derivative scalar-tensor theories in d+1 spacetime dimensions, Phys. Rev. D 108, 084018 (2023).
  103. M. Corman, J. L. Ripley, and W. E. East, Nonlinear studies of binary black hole mergers in Einstein-scalar-Gauss-Bonnet gravity, Phys. Rev. D 107, 024014 (2023).
  104. M. Corman and W. E. East, Black hole-neutron star mergers in Einstein-scalar-Gauss-Bonnet gravity, Phys. Rev. D 110, 084065 (2024).
  105. L. Aresté Saló, D. D. Doneva, K. Clough, P. Figueras, and S. S. Yazadjiev, Challenges in the nonlinear evolution of unequal mass binaries in scalar-Gauss-Bonnet gravity, Phys. Rev. D 112, 084022 (2025).
  106. G. Lara et al., Signatures from metastable oppositely-charged black hole binaries in scalar Gauss-Bonnet gravity, arXiv:2505.14785.
  107. M. Corman, L. Aresté Saló, and K. Clough, Black hole binaries in shift-symmetric Einstein-scalar-Gauss-Bonnet gravity experience a slower merger phase, arXiv:2511.19073.
  108. L. Capuano, L. Aresté Saló, D. D. Doneva, S. S. Yazadjiev, and E. Barausse, Dynamical hair growth in black hole binaries in Einstein-scalar-Gauss-Bonnet gravity, Phys. Rev. D 113, 124038 (2026).
  109. R. H. Dicke, Experimental relativity, in Les Houches Summer Shcool of Theoretical Physics: Relativity, Groups and Topology (1964), pp. 165–316.
  110. E. Poisson and C. M. Will, Gravity: Newtonian, Post-Newtonian, Relativistic (Cambridge University Press, Cambridge, England, 2014).
  111. T. P. Sotiriou, Gravity and scalar fields, in Modifications of Einstein’s Theory of Gravity at Large Distances, edited by E. Papantonopoulos (Springer International Publishing, Cham, 2015), pp. 3–24.
  112. C. M. Will, Theory and Experiment in Gravitational Physics, 2nd ed. (Cambridge University Press, Cambridge, England, 2018).
  113. M. Coleman Miller and N. Yunes, Gravitational Waves in Physics and Astrophysics (IOP, 2021), 12.
  114. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (Wiley, New York, 1972).
  115. R. M. Wald, General Relativity (Chicago University Press, Chicago, USA, 1984).
  116. C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (W. H. Freeman, San Francisco, 1973).
  117. S. M. Carroll, Spacetime and Geometry: An Introduction to General Relativity (Cambridge University Press, Cambridge, England, 2019).
  118. M. Maggiore, Gravitational Waves: Volume 1: Theory and Experiments (Oxford University Press, New York, 2007), 10.
  119. E. E. Flanagan and S. A. Hughes, The basics of gravitational wave theory, New J. Phys. 7, 204 (2005).
  120. S. Hou, Y. Gong, and Y. Liu, Polarizations of gravitational waves in Horndeski theory, Eur. Phys. J. C 78, 378 (2018).
  121. R. A. Isaacson, Gravitational radiation in the limit of high frequency. I. The linear approximation and geometrical optics, Phys. Rev. 166, 1263 (1968).
  122. R. A. Isaacson, Gravitational radiation in the limit of high frequency. II. Nonlinear terms and the effective stress tensor, Phys. Rev. 166, 1272 (1968).
  123. M. Turner, Gravitational radiation from point-masses in unbound orbits: Newtonian results, Astrophys. J. 216, 610 (1977).
  124. V. Braginsky and K. Thorne, Gravitational-wave bursts with memory and experimental prospects, Nature (London) 327, 123 (1987).
  125. D. Merritt, M. Milosavljevic, M. Favata, S. A. Hughes, and D. E. Holz, Consequences of gravitational radiation recoil, Astrophys. J. Lett. 607, L9 (2004).
  126. J. A. Gonzalez, U. Sperhake, B. Bruegmann, M. Hannam, and S. Husa, Total recoil: The maximum kick from nonspinning black-hole binary inspiral, Phys. Rev. Lett. 98, 091101 (2007).
  127. M. Favata, Gravitational-wave memory revisited: Memory from the merger and recoil of binary black holes, J. Phys. Conf. Ser. 154, 012043 (2009).
  128. M. Favata, Post-Newtonian corrections to the gravitational-wave memory for quasi-circular, inspiralling compact binaries, Phys. Rev. D 80, 024002 (2009).
  129. M. Favata, The gravitational-wave memory effect, Classical Quantum Gravity 27, 084036 (2010).
  130. A. Borchers and F. Ohme, Black-hole kicks: A tool to measure the accuracy of gravitational-wave models, in 55th Rencontres de Moriond on Gravitation (2021) 6; arXiv:2106.02414.
  131. V. Varma, S. Biscoveanu, T. Islam, F. H. Shaik, C.-J. Haster, M. Isi, W. M. Farr, S. E. Field, and S. Vitale, Evidence of large recoil velocity from a black hole merger signal, Phys. Rev. Lett. 128, 191102 (2022).
  132. F. D’Ambrosio, F. Gozzini, L. Heisenberg, H. Inchauspé, D. Maibach, and J. Zosso, Testing gravitational waveforms in full general relativity, J. Cosmol. Astropart. Phys. 02 (2025) 060.
  133. T. Kobayashi, M. Yamaguchi, and J. Yokoyama, Generalized G-inflation: Inflation with the most general second-order field equations, Prog. Theor. Phys. 126, 511 (2011).
  134. F.-L. Julié, Dynamical scalarization in Schwarzschild binary inspirals, arXiv:2312.16764.
  135. K. Yagi, L. C. Stein, N. Yunes, and T. Tanaka, Post-Newtonian, quasi-circular binary inspirals in quadratic modified gravity, Phys. Rev. D 85, 064022 (2012); 93, 029902(E) (2016).
  136. L. Aresté Saló, S. E. Brady, K. Clough, D. Doneva, T. Evstafyeva, P. Figueras, T. França, L. Rossi, and S. Yao, GRFolres: A code for modified gravity simulations in strong gravity, J. Open Source Software 9, 6369 (2024).
  137. T. Andrade et al., GRChombo: An adaptable numerical relativity code for fundamental physics, J. Open Source Software 6, 3703 (2021).
  138. M. Ansorg, B. Bruegmann, and W. Tichy, A Single-domain spectral method for black hole puncture data, Phys. Rev. D 70, 064011 (2004).
  139. E. Barausse, C. Palenzuela, M. Ponce, and L. Lehner, Neutron-star mergers in scalar-tensor theories of gravity, Phys. Rev. D 87, 081506 (2013).
  140. M. Shibata, K. Taniguchi, H. Okawa, and A. Buonanno, Coalescence of binary neutron stars in a scalar-tensor theory of gravity, Phys. Rev. D 89, 084005 (2014).
  141. E. M. Sänger et al., Tests of general relativity with GW230529: A neutron star merging with a lower mass-gap compact object, Phys. Rev. D 113, 084070 (2026).
  142. V. I. Danchev, D. D. Doneva, and S. S. Yazadjiev, Constraining scalarization in scalar-Gauss-Bonnet gravity through binary pulsars, Phys. Rev. D 106, 124001 (2022).
  143. P. Y. Yordanov, K. V. Staykov, S. S. Yazadjiev, and D. D. Doneva, The power of binary pulsars in testing Gauss-Bonnet gravity, Astron. Astrophys. 687, A17 (2024).
  144. L. K. Wong, C. A. R. Herdeiro, and E. Radu, Constraining spontaneous black hole scalarization in scalar-tensor-Gauss-Bonnet theories with current gravitational-wave data, Phys. Rev. D 106, 024008 (2022).
  145. E. Berti, V. Cardoso, J. A. Gonzalez, U. Sperhake, M. Hannam, S. Husa, and B. Bruegmann, Inspiral, merger and ringdown of unequal mass black hole binaries: A multipolar analysis, Phys. Rev. D 76, 064034 (2007).
  146. V. Varma, S. E. Field, M. A. Scheel, J. Blackman, L. E. Kidder, and H. P. Pfeiffer, Surrogate model of hybridized numerical relativity binary black hole waveforms, Phys. Rev. D 99, 064045 (2019).
  147. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Properties of the binary black hole merger GW150914, Phys. Rev. Lett. 116, 241102 (2016).
  148. F.-L. Julié, L. Pompili, and A. Buonanno, Inspiral-merger-ringdown waveforms in Einstein-scalar-Gauss-Bonnet gravity within the effective-one-body formalism, Phys. Rev. D 111, 024016 (2025).
  149. 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).
  150. 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).
  151. M. Pürrer and C.-J. Haster, Gravitational waveform accuracy requirements for future ground-based detectors, Phys. Rev. Res. 2, 023151 (2020).
  152. R. Abbott et al. (KAGRA, Virgo, and LIGO Scientific Collaborations), Population of merging compact binaries inferred using gravitational waves through GWTC-3, Phys. Rev. X 13, 011048 (2023).
  153. A. G. Abac et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), GWTC-4.0: Population properties of merging compact binaries, Astrophys. J. Lett. 1005, L51 (2026).
  154. S. Hild et al., Sensitivity studies for third-generation gravitational wave observatories, Classical Quantum Gravity 28, 094013 (2011).
  155. B. Goncharov, L. Donnay, and J. Harms, Inferring fundamental spacetime symmetries with gravitational-wave memory: From LISA to the Einstein telescope, Phys. Rev. Lett. 132, 241401 (2024).
  156. A. Maselli, S. Yi, L. Pierini, V. Vellucci, L. Reali, L. Gualtieri, and E. Berti, Black hole spectroscopy beyond Kerr: Agnostic and theory-based tests with next-generation interferometers, Phys. Rev. D 109, 064060 (2024).
  157. A. T.-L. Lam, Y. Gao, H.-J. Kuan, M. Shibata, K. Van Aelst, and K. Kiuchi, Accessing universal relations of binary neutron star waveforms in massive scalar-tensor theory, Phys. Rev. Lett. 134, 151402 (2025).
  158. W. E. East and F. Pretorius, Binary neutron star mergers in Einstein-scalar-Gauss-Bonnet gravity, Phys. Rev. D 106, 104055 (2022).
  159. L. Aresté Saló, R. Aguilera-Miret, M. Bezares, and T. P. Sotiriou, From mergers to collapse: Scalarisation dynamics in neutron star binaries, arXiv:2602.10755.
  160. S. Ma, V. Varma, L. C. Stein, F. Foucart, M. D. Duez, L. E. Kidder, H. P. Pfeiffer, and M. A. Scheel, Numerical simulations of black hole-neutron star mergers in scalar-tensor gravity, Phys. Rev. D 107, 124051 (2023).
  161. N. T. Bishop, R. Gomez, L. Lehner, and J. Winicour, Cauchy-characteristic extraction in numerical relativity, Phys. Rev. D 54, 6153 (1996).
  162. K. Mitman, J. Moxon, M. A. Scheel, S. A. Teukolsky, M. Boyle, N. Deppe, L. E. Kidder, and W. Throwe, Computation of displacement and spin gravitational memory in numerical relativity, Phys. Rev. D 102, 104007 (2020).
  163. K. Mitman et al., A review of gravitational memory and BMS frame fixing in numerical relativity, Classical Quantum Gravity 41, 223001 (2024).

Outline

Information

Phys. Rev. D 114, 044094– Published 26 August, 2026
  • Received 20 April 2026
  • Revised 15 July 2026
  • Accepted 20 July 2026
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. Open access publication funded by CERN.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation