- Open Access
Challenges in the nonlinear evolution of unequal mass binaries in scalar-Gauss-Bonnet gravity
Phys. Rev. D 112, 084022 – Published 8 October, 2025
DOI: https://doi.org/10.1103/tr7v-jhhm
Abstract
It has only recently become possible to simulate the full nonlinear dynamics of binary black holes in scalar-Gauss-Bonnet theories of gravity. The simulations remain technically challenging and evolutions of unequal mass binaries in particular have been difficult to follow through the merger. Even when the merger is successful, accurately quantifying the physical dephasing, as opposed to contributions from transients in the initial data and gauge adjustments, remains difficult. We show the first full simulations of and binaries through merger, and we discuss how specific choices in the setup affect the dephasing observed and our ability to obtain reliable results. In cases with weaker couplings, we match the expected PN value for the dephasing, whereas for larger couplings, eccentricity introduced by the initial data transients can lead to artificial deviations. Our work highlights the need for improvements in the initial data methods used, to ensure reliable waveforms are obtained for data analysis in beyond-GR models.
Physics Subject Headings (PhySH)
Article Text
References (90)
- B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Observation of gravitational waves from a binary black hole merger, Phys. Rev. Lett. 116, 061102 (2016).
- B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Tests of general relativity with the binary black hole signals from the LIGO-Virgo catalog GWTC-1, Phys. Rev. D 100, 104036 (2019).
- R. Abbott et al. (LIGO Scientific and Virgo Collaborations), Tests of general relativity with binary black holes from the second LIGO-Virgo gravitational-wave transient catalog, Phys. Rev. D 103, 122002 (2021).
- R. Abbott et al. (LIGO Scientific, VIRGO, and KAGRA Collaborations), Tests of general relativity with GWTC-3, arXiv:2112.06861.
- P. Amaro-Seoane et al. (LISA Collaboration), Laser interferometer space antenna, arXiv:1702.00786.
- M. Punturo et al., The Einstein Telescope: A third-generation gravitational wave observatory, Classical Quantum Gravity 27, 194002 (2010).
- M. Maggiore et al. (ET Collaboration), Science case for the Einstein Telescope, J. Cosmol. Astropart. Phys. 03 (2020) 050.
- D. Reitze et al., Cosmic explorer: The U.S. contribution to gravitational-wave astronomy beyond LIGO, Bull. Am. Astron. Soc. 51, 035 (2019).
- K. G. Arun et al. (LISA Collaboration), New horizons for fundamental physics with LISA, Living Rev. Relativity 25, 4 (2022).
- S. E. Perkins, N. Yunes, and E. Berti, Probing fundamental physics with gravitational waves: The next generation, Phys. Rev. D 103, 044024 (2021).
- E. Barausse et al., Prospects for fundamental physics with LISA, Gen. Relativ. Gravit. 52, 81 (2020).
- 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).
- L. Barack et al., Black holes, gravitational waves and fundamental physics: A roadmap, Classical Quantum Gravity 36, 143001 (2019).
- 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).
- E. Maggio, H. O. Silva, A. Buonanno, and A. Ghosh, Tests of general relativity in the nonlinear regime: A parametrized plunge-merger-ringdown gravitational waveform model, Phys. Rev. D 108, 024043 (2023).
- L. Pompili, E. Maggio, H. O. Silva, and A. Buonanno, Parametrized spin-precessing inspiral-merger-ringdown waveform model for tests of general relativity, Phys. Rev. D 111, 124040 (2025).
- N. V. Krishnendu and F. Ohme, Testing general relativity with gravitational waves: An overview, Universe 7, 497 (2021).
- Z. Carson and K. Yagi, Parametrized and inspiral-merger-ringdown consistency tests of gravity with multiband gravitational wave observations, Phys. Rev. D 101, 044047 (2020).
- N. Cornish, L. Sampson, N. Yunes, and F. Pretorius, Gravitational wave tests of general relativity with the parameterized post-Einsteinian framework, Phys. Rev. D 84, 062003 (2011).
- J. E. Thompson, E. Hamilton, L. London, S. Ghosh, P. Kolitsidou, C. Hoy, and M. Hannam, PhenomXO4a: A phenomenological gravitational-wave model for precessing black-hole binaries with higher multipoles and asymmetries, Phys. Rev. D 109, 063012 (2024).
- S. Ghosh, P. Kolitsidou, and M. Hannam, First frequency-domain phenomenological model of the multipole asymmetry in gravitational-wave signals from binary-black-hole coalescence, Phys. Rev. D 109, 024061 (2024).
- 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).
- 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).
- A. Dhani, S. Völkel, A. Buonanno, H. Estellés, 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, Phys. Rev. X 15, 031036 (2025).
- 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, Phys. Rev. Lett. 134, 251402 (2025).
- A. D. Kovács and H. S. Reall, Well-posed formulation of scalar-tensor effective field theory, Phys. Rev. Lett. 124, 221101 (2020).
- A. D. Kovács and H. S. Reall, Well-posed formulation of Lovelock and Horndeski theories, Phys. Rev. D 101, 124003 (2020).
- 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).
- L. Aresté Saló, K. Clough, and P. Figueras, Puncture gauge formulation for Einstein-Gauss-Bonnet gravity and four-derivative scalar-tensor theories in spacetime dimensions, Phys. Rev. D 108, 084018 (2023).
- J. Healy, T. Bode, R. Haas, E. Pazos, P. Laguna, D. Shoemaker, and N. Yunes, Late inspiral and merger of binary black holes in scalar-tensor theories of gravity, Classical Quantum Gravity 29, 232002 (2012).
- 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).
- T. Torii, H. Yajima, and K.-i. Maeda, Dilatonic black holes with Gauss-Bonnet term, Phys. Rev. D 55, 739 (1997).
- T. P. Sotiriou and S.-Y. Zhou, Black hole hair in generalized scalar-tensor gravity, Phys. Rev. Lett. 112, 251102 (2014).
- 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).
- 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).
- 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).
- B. Kleihaus, J. Kunz, S. Mojica, and E. Radu, Spinning black holes in Einstein–Gauss-Bonnet–Dilaton theory: Nonperturbative solutions, Phys. Rev. D 93, 044047 (2016).
- B. Kleihaus, J. Kunz, and E. Radu, Rotating black holes in dilatonic Einstein-Gauss-Bonnet theory, Phys. Rev. Lett. 106, 151104 (2011).
- 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).
- 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).
- 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).
- 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).
- J. L. Ripley and F. Pretorius, Scalarized black hole dynamics in Einstein dilaton Gauss-Bonnet gravity, Phys. Rev. D 101, 044015 (2020).
- 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).
- D. D. Doneva, L. Aresté Saló, and S. S. Yazadjiev, nonlinear evolution of Ricci-coupled scalar-Gauss-Bonnet gravity, Phys. Rev. D 110, 024040 (2024).
- 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).
- F. Thaalba, N. Franchini, M. Bezares, and T. P. Sotiriou, Hyperbolicity in scalar-Gauss-Bonnet gravity: A gauge invariant study for spherical evolution, Phys. Rev. D 111, 024053 (2025).
- F. Thaalba, N. Franchini, M. Bezares, and T. P. Sotiriou, Dynamics of spherically symmetric black holes in scalar-Gauss-Bonnet gravity with a Ricci coupling, Phys. Rev. D 111, 064054 (2025).
- F. Thaalba, M. Bezares, N. Franchini, and T. P. Sotiriou, Spherical collapse in scalar-Gauss-Bonnet gravity: Taming ill-posedness with a Ricci coupling, Phys. Rev. D 109, L041503 (2024).
- N. Franchini, M. Bezares, E. Barausse, and L. Lehner, Fixing the dynamical evolution in scalar-Gauss-Bonnet gravity, Phys. Rev. D 106, 064061 (2022).
- 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).
- M. Corman and W. E. East, Black hole-neutron star mergers in Einstein-scalar-Gauss-Bonnet gravity, Phys. Rev. D 110, 084065 (2024).
- W. E. East and F. Pretorius, Binary neutron star mergers in Einstein-scalar-Gauss-Bonnet gravity, Phys. Rev. D 106, 104055 (2022).
- 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).
- M. Corman, L. Lehner, W. E. East, and G. Dideron, Nonlinear studies of modifications to general relativity: Comparing different approaches, Phys. Rev. D 110, 084048 (2024).
- A. H. K. R, J. L. Ripley, and N. Yunes, Where and why does Einstein-scalar-Gauss-Bonnet theory break down?, Phys. Rev. D 107, 044044 (2023).
- M. Okounkova, L. C. Stein, M. A. Scheel, and D. A. Hemberger, Numerical binary black hole mergers in dynamical Chern-Simons gravity: Scalar field, Phys. Rev. D 96, 044020 (2017).
- H. O. Silva, H. Witek, M. Elley, and N. Yunes, Dynamical descalarization in binary black hole mergers, Phys. Rev. Lett. 127, 031101 (2021).
- M. Elley, H. O. Silva, H. Witek, and N. Yunes, Spin-induced dynamical scalarization, descalarization, and stealthness in scalar-Gauss-Bonnet gravity during a black hole coalescence, Phys. Rev. D 106, 044018 (2022).
- D. D. Doneva, A. Vañó Viñuales, and S. S. Yazadjiev, Dynamical descalarization with a jump during a black hole merger, Phys. Rev. D 106, L061502 (2022).
- T. Evstafyeva, M. Agathos, and J. L. Ripley, Measuring the ringdown scalar polarization of gravitational waves in Einstein-scalar-Gauss-Bonnet gravity, Phys. Rev. D 107, 124010 (2023).
- B. Shiralilou, T. Hinderer, S. Nissanke, N. Ortiz, and H. Witek, Nonlinear curvature effects in gravitational waves from inspiralling black hole binaries, Phys. Rev. D 103, L121503 (2021).
- B. Shiralilou, T. Hinderer, S. M. Nissanke, N. Ortiz, and H. Witek, Post-Newtonian gravitational and scalar waves in scalar-Gauss–Bonnet gravity, Classical Quantum Gravity 39, 035002 (2022).
- F.-L. Julié and E. Berti, Post-Newtonian dynamics and black hole thermodynamics in Einstein-scalar-Gauss-Bonnet gravity, Phys. Rev. D 100, 104061 (2019).
- 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).
- 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).
- G. Lara et al., Signatures from metastable oppositely-charged black hole binaries in scalar Gauss-Bonnet gravity, arXiv:2505.14785.
- S. E. Brady, L. Aresté Saló, K. Clough, P. Figueras, and A. P. S., Solving the initial conditions problem for modified gravity theories, Phys. Rev. D 108, 104022 (2023).
- P. J. Nee, G. Lara, H. P. Pfeiffer, and N. L. Vu, Quasistationary hair for binary black hole initial data in scalar Gauss-Bonnet gravity, Phys. Rev. D 111, 024061 (2025).
- R. M. Wald, General Relativity (Chicago University Press, Chicago, USA, 1984).
- D. Alic, C. Bona-Casas, C. Bona, L. Rezzolla, and C. Palenzuela, Conformal and covariant formulation of the Z4 system with constraint-violation damping, Phys. Rev. D 85, 064040 (2012).
- 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 Softwaare 9, 6369 (2024).
- T. Andrade et al., grchombo: An adaptable numerical relativity code for fundamental physics, J. Open Source Softwaare 6, 3703 (2021).
- M. Radia, U. Sperhake, A. Drew, K. Clough, P. Figueras, E. A. Lim, J. L. Ripley, J. C. Aurrekoetxea, T. França, and T. Helfer, Lessons for adaptive mesh refinement in numerical relativity, Classical Quantum Gravity 39, 135006 (2022).
- M. Ansorg, B. Brügmann, and W. Tichy, A single-domain spectral method for black hole puncture data, Phys. Rev. D 70, 064011 (2004).
- B. Brügmann, J. A. González, M. Hannam, S. Husa, U. Sperhake, and W. Tichy, Calibration of moving puncture simulations, Phys. Rev. D 77, 024027 (2008).
- D. Ferguson et al., Second MAYA catalog of binary black hole numerical relativity waveforms, Phys. Rev. D 112, 044043 (2025).
- H. Witek, L. Gualtieri, and P. Pani, Towards numerical relativity in scalar Gauss-Bonnet gravity: decomposition beyond the small-coupling limit, Phys. Rev. D 101, 124055 (2020).
- N. Sennett, S. Marsat, and A. Buonanno, Gravitational waveforms in scalar-tensor gravity at 2PN relative order, Phys. Rev. D 94, 084003 (2016).
- 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).
- D. Müller, J. Grigsby, and B. Brügmann, Dynamical shift condition for unequal mass black hole binaries, Phys. Rev. D 82, 064004 (2010).
- L. Aresté Saló, M. Corman, and K. Clough, GH3d2M versus grfolres (to be published).
- 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).
- 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).
- 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, arXiv:2412.09377.
- M. H.-Y. Cheung, E. Berti, V. Baibhav, and R. Cotesta, Extracting linear and nonlinear quasinormal modes from black hole merger simulations, Phys. Rev. D 109, 044069 (2024); 110, 049902(E) (2024).
- H. P. Pfeiffer, D. A. Brown, L. E. Kidder, L. Lindblom, G. Lovelace, and M. A. Scheel, Reducing orbital eccentricity in binary black hole simulations, Classical Quantum Gravity 24, S59 (2007).
- www.grtlcollaboration.org
- www.dirac.ac.uk
- A. H. Mroue, H. P. Pfeiffer, L. E. Kidder, and S. A. Teukolsky, Measuring orbital eccentricity and periastron advance in quasi-circular black hole simulations, Phys. Rev. D 82, 124016 (2010).