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Well-posed BSSN-type formulation for scalar-tensor theories of gravity with second-order field equations

Harry L. H. Shum1,2, Llibert Aresté Saló3,4, Farid Thaalba1,2,5, Miguel Bezares1,2, and Thomas P. Sotiriou1,2,6

  • 1Nottingham Centre of Gravity, Nottingham NG7 2RD, United Kingdom
  • 2School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
  • 3Instituut voor Theoretische Fysica, KU Leuven. Celestijnenlaan 200D, B-3001 Leuven, Belgium
  • 4Leuven Gravity Institute, KU Leuven. Celestijnenlaan 200D, B-3001 Leuven, Belgium
  • 5SISSA, via Bonomea 265, 34136 Trieste, Italy and INFN (Sez. Trieste), via Valerio 2, 34127 Trieste, Italy
  • 6School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom

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Phys. Rev. D 113, 104001 – Published 4 May, 2026

DOI: https://doi.org/10.1103/fyvl-p35y

Abstract

Recent developments in the modified harmonic and modified puncture gauges have opened new possibilities for performing stable numerical evolutions beyond General Relativity. In this work, we utilize techniques developed in the aforementioned formalisms to derive a BSSN-type formalism compatible with certain classes of modified gravity theories. As an intermediate step, we also derived modified versions of the Z4 and Z3 formalisms, thereby completing the connection between these formalisms beyond General Relativity. We then test the robustness of the new modified BSSN formalism by simulating the dynamics of black hole systems and benchmarking the results against the modified CCZ4 formulation. These developments enable the exploration of theories beyond General Relativity in many well-known numerical relativity codes that use different versions of the puncture gauge approach.

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Phys. Rev. D 113, 104001– Published 4 May, 2026
  • Received 6 January 2026
  • Accepted 3 April 2026
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