- 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

Extreme mass ratio head-on collisions of black holes in Einstein-scalar-Gauss-Bonnet theory

Antonia M. Frassino1,2,3,4, David C. Lopes5, and Jorge V. Rocha4,6,7

PDF

Phys. Rev. D 114, 104046 – Published 12 November, 2026

DOI: https://doi.org/10.1103/twfc-xd1g

Abstract

The evolution of the event horizon when two black holes merge can be determined by resorting to ray-tracing techniques on a single black hole spacetime, under the assumption that the binary’s mass ratio is infinite and the underlying gravity theory respects the equivalence principle. We extend this analysis to the collision of nonspinning hairy black holes in Einstein-scalar-Gauss-Bonnet gravity. In such theories the scalar field is coupled to a higher curvature operator, leading to possible modifications of the background geometry and consequently of photon propagation. We study three families of coupling functions: linear, quadratic, and a particular exponential form. The first choice enjoys a shift symmetry and forces the presence of scalar hair in the spectrum of black hole solutions. The latter two couplings break the shift symmetry and allow for spontaneously scalarized hairy black holes, which coexist with the Schwarzschild black hole. For all three classes of theories studied, we find a merger duration that is longer than the corresponding time in general relativity, when keeping the size of the small black hole fixed and for viably small values of the coupling constant. However, the case of the exponential coupling yields a nonmonotonic merger duration, which can become shorter than the general relativity value for a sufficiently large coupling constant. We observe that the merger duration and the area increment generically track the behavior of the small black hole’s photon ring. Finally, we also compare our results with recent numerical simulations by other groups, despite the dissimilar mass ratios considered.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (96)

  1. K. G. Arun et al. (LISA Collaboration), New horizons for fundamental physics with LISA, Living Rev. Relativity 25, 4 (2022).
  2. L. Barack et al., Black holes, gravitational waves and fundamental physics: A roadmap, Classical Quantum Gravity 36, 143001 (2019).
  3. G. Gnocchi, A. Maselli, T. Abdelsalhin, N. Giacobbo, and M. Mapelli, Bounding alternative theories of gravity with multiband GW observations, Phys. Rev. D 100, 064024 (2019).
  4. T. Baker, D. Psaltis, and C. Skordis, Linking tests of gravity on all scales: From the strong-field regime to cosmology, Astrophys. J. 802, 63 (2015).
  5. A. G. Abac et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), Open data from LIGO, Virgo, and KAGRA through the first part of the fourth observing run, Astrophys. J. 1004, 232 (2026).
  6. A. G. Abac et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), Directional search for persistent gravitational waves: Results from the first part of LIGO-Virgo-KAGRA’s fourth observing run, Phys. Rev. D 114, 022001 (2026).
  7. P. Amaro-Seoane et al., Laser Interferometer Space Antenna, arXiv:1702.00786.
  8. M. Punturo et al., The Einstein Telescope: A third-generation gravitational wave observatory, Classical Quantum Gravity 27, 194002 (2010).
  9. M. Maggiore et al. (ET Collaboration), Science case for the Einstein Telescope, J. Cosmol. Astropart. Phys. 03 (2020) 050.
  10. D. Reitze et al., Cosmic Explorer: The U.S. Contribution to gravitational-wave astronomy beyond LIGO, Bull. Am. Astron. Soc. 51, 035 (2019).
  11. LIGO Scientific, Virgo, and KAGRA Collaborations, Black hole spectroscopy and tests of general relativity with GW250114, Phys. Rev. Lett. 136, 041403 (2026).
  12. A. G. Abac et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), GW250114: Testing Hawking’s area law and the Kerr nature of black holes, Phys. Rev. Lett. 135, 111403 (2025).
  13. E. Berti et al., Testing general relativity with present and future astrophysical observations, Classical Quantum Gravity 32, 243001 (2015).
  14. G. W. Horndeski, Second-order scalar-tensor field equations in a four-dimensional space, Int. J. Theor. Phys. 10, 363 (1974).
  15. 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).
  16. 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).
  17. T. P. Sotiriou and S.-Y. Zhou, Black hole hair in generalized scalar-tensor gravity, Phys. Rev. Lett. 112, 251102 (2014).
  18. T. P. Sotiriou and S.-Y. Zhou, Black hole hair in generalized scalar-tensor gravity: An explicit example, Phys. Rev. D 90, 124063 (2014).
  19. 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).
  20. 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).
  21. 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).
  22. G. Antoniou, A. Bakopoulos, and P. Kanti, Black-hole solutions with scalar hair in Einstein-scalar-Gauss-Bonnet theories, Phys. Rev. D 97, 084037 (2018).
  23. T. Damour and G. Esposito-Farèse, Nonperturbative strong field effects in tensor-scalar theories of gravitation, Phys. Rev. Lett. 70, 2220 (1993).
  24. T. Damour and G. Esposito-Farèse, Tensor-scalar gravity and binary pulsar experiments, Phys. Rev. D 54, 1474 (1996).
  25. 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).
  26. L. Amendola, C. Charmousis, and S. C. Davis, Solar system constraints on Gauss-Bonnet mediated dark energy, J. Cosmol. Astropart. Phys. 10 (2007) 004.
  27. B. Elder and J. Sakstein, Mapping the weak field limit of scalar-Gauss-Bonnet gravity, Phys. Rev. D 107, 044006 (2023).
  28. H. Witek, L. Gualtieri, P. Pani, and T. P. Sotiriou, Black holes and binary mergers in scalar Gauss-Bonnet gravity: Scalar field dynamics, Phys. Rev. D 99, 064035 (2019).
  29. M. Okounkova, Numerical relativity simulation of GW150914 in Einstein dilaton Gauss-Bonnet gravity, Phys. Rev. D 102, 084046 (2020).
  30. R. Nair, S. Perkins, H. O. Silva, and N. Yunes, Fundamental physics implications for higher-curvature theories from binary black hole signals in the LIGO-Virgo catalog GWTC-1, Phys. Rev. Lett. 123, 191101 (2019).
  31. Z. Carson, B. C. Seymour, and K. Yagi, Future prospects for probing scalar–tensor theories with gravitational waves from mixed binaries, Classical Quantum Gravity 37, 065008 (2020).
  32. S. E. Perkins, R. Nair, H. O. Silva, and N. Yunes, Improved gravitational-wave constraints on higher-order curvature theories of gravity, Phys. Rev. D 104, 024060 (2021).
  33. Z. Lyu, N. Jiang, and K. Yagi, Constraints on Einstein-dilation-Gauss-Bonnet gravity from black hole-neutron star gravitational wave events, Phys. Rev. D 105, 064001 (2022); 106, 069901(E) (2022).
  34. 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).
  35. 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).
  36. 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).
  37. 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).
  38. 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).
  39. Á. D. Kovács and H. S. Reall, Well-posed formulation of scalar-tensor effective field theory, Phys. Rev. Lett. 124, 221101 (2020).
  40. P. Figueras, A. Held, and Á. D. Kovács, Well-posed initial value formulation of general effective field theories of gravity, arXiv:2407.08775.
  41. 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).
  42. 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).
  43. 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).
  44. D. D. Doneva, L. Aresté Saló, K. Clough, P. Figueras, and S. S. Yazadjiev, Testing the limits of scalar-Gauss-Bonnet gravity through nonlinear evolutions of spin-induced scalarization, Phys. Rev. D 108, 084017 (2023).
  45. L. Aresté Saló, D. D. Doneva, K. Clough, P. Figueras, and S. S. Yazadjiev, Challenges in the nonlinear evolution of unequal mass binaries in sGB gravity, Phys. Rev. D 112, 084022 (2025).
  46. 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.
  47. R. Emparan and M. Martínez, Exact event horizon of a black hole merger, Classical Quantum Gravity 33, 155003 (2016).
  48. R. Emparan and M. Martínez, Black hole fusion made easy, Int. J. Mod. Phys. D 25, 1644015 (2016).
  49. R. Emparan, M. Martínez, and M. Zilhão, Black hole fusion in the extreme mass ratio limit, Phys. Rev. D 97, 044004 (2018).
  50. R. Emparan and D. Marín, Precursory collapse in neutron star-black hole mergers, Phys. Rev. D 102, 024009 (2020).
  51. D. M. Pina, M. Orselli, and D. Pica, Event horizon of a charged black hole binary merger, Phys. Rev. D 106, 084012 (2022).
  52. J. M. Dias, A. M. Frassino, V. D. Paccoia, and J. V. Rocha, Black hole-wormhole collisions and the emergence of islands, Phys. Rev. D 107, 124056 (2023).
  53. M. Gadioux, R. A. Hennigar, and H. S. Reall, Evolution of creases on the event horizon of a black hole merger, Phys. Rev. D 110, 084029 (2024).
  54. J. M. Dias, A. M. Frassino, D. C. Lopes, V. D. Paccoia, and J. V. Rocha, Impact of higher derivative corrections to general relativity on black hole mergers, Phys. Rev. D 110, 124025 (2024).
  55. M. Gadioux and H. Wang, The merger of a black hole with a cosmological horizon, Classical Quantum Gravity 42, 095010 (2025).
  56. M. G. Richarte and J. D. Toniato, Exploring scalarized Einstein-Gauss-Bonnet theories through the lens of parametrized post-Newtonian formalism, Phys. Rev. D 112, 024019 (2025).
  57. M. G. Richarte and J. D. Toniato, In-depth analysis of violations of the strong equivalence principle in scalarized Einstein-Gauss-Bonnet theories, Phys. Rev. D 112, 084058 (2025).
  58. 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).
  59. K. Yagi, L. C. Stein, and N. Yunes, Challenging the presence of scalar charge and dipolar radiation in binary pulsars, Phys. Rev. D 93, 024010 (2016).
  60. J. F. Donoghue, General relativity as an effective field theory: The leading quantum corrections, Phys. Rev. D 50, 3874 (1994).
  61. C. P. Burgess, Quantum gravity in everyday life: General relativity as an effective field theory, Living Rev. Relativity 7, 5 (2004).
  62. S. Weinberg, Effective field theory for inflation, Phys. Rev. D 77, 123541 (2008).
  63. D. J. Gross and J. H. Sloan, The quartic effective action for the heterotic string, Nucl. Phys. B291, 41 (1987).
  64. 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).
  65. S. Nojiri, S. D. Odintsov, and M. Sasaki, Gauss-Bonnet dark energy, Phys. Rev. D 71, 123509 (2005).
  66. J. F. M. Delgado, C. A. R. Herdeiro, and E. Radu, Spinning black holes in shift-symmetric Horndeski theory, J. High Energy Phys. 04 (2020) 180.
  67. M. Minamitsuji, K. Takahashi, and S. Tsujikawa, Linear stability of black holes in shift-symmetric Horndeski theories with a time-independent scalar field, Phys. Rev. D 105, 104001 (2022).
  68. A. K.-W. Chung and N. Yunes, Quasinormal mode frequencies and gravitational perturbations of black holes with any subextremal spin in modified gravity through METRICS: The scalar-Gauss-Bonnet gravity case, Phys. Rev. D 110, 064019 (2024).
  69. F. S. Khoo, J. L. Blázquez-Salcedo, B. Kleihaus, and J. Kunz, Quasinormal modes of rotating black holes in shift-symmetric Einstein-scalar-Gauss–Bonnet theory, Eur. Phys. J. C 85, 1366 (2025).
  70. A. G. Abac et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), GWTC-5.0: Population properties of merging compact binaries, arXiv:2605.27226.
  71. J. L. Blázquez-Salcedo, D. D. Doneva, J. Kunz, and S. S. Yazadjiev, Radial perturbations of the scalarized Einstein-Gauss-Bonnet black holes, Phys. Rev. D 98, 084011 (2018).
  72. H. O. Silva, C. F. B. Macedo, T. P. Sotiriou, L. Gualtieri, J. Sakstein, and E. Berti, Stability of scalarized black hole solutions in scalar-Gauss-Bonnet gravity, Phys. Rev. D 99, 064011 (2019).
  73. M. Minamitsuji and T. Ikeda, Scalarized black holes in the presence of the coupling to Gauss-Bonnet gravity, Phys. Rev. D 99, 044017 (2019).
  74. J. L. Blázquez-Salcedo, D. D. Doneva, S. Kahlen, J. Kunz, P. Nedkova, and S. S. Yazadjiev, Polar quasinormal modes of the scalarized Einstein-Gauss-Bonnet black holes, Phys. Rev. D 102, 024086 (2020).
  75. J. L. Blázquez-Salcedo, D. D. Doneva, S. Kahlen, J. Kunz, P. Nedkova, and S. S. Yazadjiev, Axial perturbations of the scalarized Einstein-Gauss-Bonnet black holes, Phys. Rev. D 101, 104006 (2020).
  76. J. Libson, J. Masso, E. Seidel, W.-M. Suen, and P. Walker, Event horizons in numerical relativity. 1: Methods and tests, Phys. Rev. D 53, 4335 (1996).
  77. J. Thornburg, Event and apparent horizon finders for 3+1 numerical relativity, Living Rev. Relativity 10, 3 (2007).
  78. J. Masso, E. Seidel, W.-M. Suen, and P. Walker, Event horizons in numerical relativity 2.: Analyzing the horizon, Phys. Rev. D 59, 064015 (1999).
  79. M. Gadioux and H. S. Reall, Creases, corners, and caustics: Properties of nonsmooth structures on black hole horizons, Phys. Rev. D 108, 084021 (2023).
  80. N. Yunes and L. C. Stein, Non-spinning black holes in alternative theories of gravity, Phys. Rev. D 83, 104002 (2011).
  81. N. Oshita, S. Ma, Y. Chen, and H. Yang, Probing direct waves in black hole ringdowns, arXiv:2509.09165.
  82. N. Lu, S. Ma, O. J. Piccinni, Y. Chen, and L. Sun, GW250114 reveals signatures of post-merger black-hole horizon, Nature (London) 655, 71 (2026).
  83. P. Bueno and P. A. Cano, Einsteinian cubic gravity, Phys. Rev. D 94, 104005 (2016).
  84. V. Ferrari and B. Mashhoon, New approach to the quasinormal modes of a black hole, Phys. Rev. D 30, 295 (1984).
  85. B. Mashhoon, Stability of charged rotating black holes in the eikonal approximation, Phys. Rev. D 31, 290 (1985).
  86. V. Cardoso, A. S. Miranda, E. Berti, H. Witek, and V. T. Zanchin, Geodesic stability, Lyapunov exponents and quasinormal modes, Phys. Rev. D 79, 064016 (2009).
  87. D. Giataganas, G. F. Giudice, A. Ianniccari, A. J. Iovino, A. Kehagias, F. Quevedo, D. Perrone, and A. Riotto, Black hole mergers as the fastest photon ring scramblers, Phys. Rev. D 114, 023556 (2026).
  88. J. L. Jaramillo, B. Krishnan, and C. F. Sopuerta, Universality in binary black hole dynamics: An integrability conjecture, Int. J. Mod. Phys. D 32, 2342005 (2023).
  89. D. Pook-Kolb, O. Birnholtz, B. Krishnan, and E. Schnetter, Self-intersecting marginally outer trapped surfaces, Phys. Rev. D 100, 084044 (2019).
  90. D. Pook-Kolb, O. Birnholtz, J. L. Jaramillo, B. Krishnan, and E. Schnetter, Horizons in a binary black hole merger I: Geometry and area increase, arXiv:2006.03939.
  91. D. Pook-Kolb, O. Birnholtz, J. L. Jaramillo, B. Krishnan, and E. Schnetter, Horizons in a binary black hole merger II: Fluxes, multipole moments and stability, arXiv:2006.03940.
  92. I. Booth, R. A. Hennigar, and S. Mondal, Marginally outer trapped surfaces in the Schwarzschild spacetime: Multiple self-intersections and extreme mass ratio mergers, Phys. Rev. D 102, 044031 (2020).
  93. D. Pook-Kolb, R. A. Hennigar, and I. Booth, What happens to apparent horizons in a binary black hole merger?, Phys. Rev. Lett. 127, 181101 (2021).
  94. K. D. Kokkotas, R. A. Konoplya, and A. Zhidenko, Analytical approximation for the Einstein-dilaton-Gauss-Bonnet black hole metric, Phys. Rev. D 96, 064004 (2017).
  95. A. Maselli, N. Franchini, L. Gualtieri, and T. P. Sotiriou, Detecting scalar fields with extreme mass ratio inspirals, Phys. Rev. Lett. 125, 141101 (2020).
  96. M. Davis, R. Ruffini, W. H. Press, and R. H. Price, Gravitational radiation from a particle falling radially into a Schwarzschild black hole, Phys. Rev. Lett. 27, 1466 (1971).

Outline

Information

Phys. Rev. D 114, 104046– Published 12 November, 2026
  • Received 29 April 2026
  • Accepted 14 September 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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation