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Well-posedness of the four-derivative scalar-tensor theory of gravity in singularity avoiding coordinates

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arxiv 2208.14470 v3 pith:M6LEVCRI submitted 2022-08-30 gr-qc hep-th

Llibert Aresté Saló , Katy Clough , Pau Figueras This is my paper
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keywords blackcoordinatescouplingcouplingsformulationgravityholescalar-tensor
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abstract

We show that the most general scalar-tensor theory of gravity up to four derivatives in $3+1$ dimensions is well-posed in a modified version of the CCZ4 formulation of the Einstein equations in singularity-avoiding coordinates. We demonstrate the robustness of our new formulation in practise by studying equal mass black hole binary mergers for different values of the coupling constants. Although our analysis of well-posedness is restricted to cases in which the couplings are small, we find that in simulations we are able to push the couplings to larger values, so that a certain weak coupling condition is order one, without instabilities developing. Our work provides the means for such simulations to be undertaken by the many numerical relativity codes that rely on the moving puncture gauge to evolve black hole singularities.

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Cited by 7 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Signatures from metastable oppositely-charged black hole binaries in scalar Gauss-Bonnet gravity

    gr-qc 2025-05 conditional novelty 7.0 of 10

    In scalar Gauss-Bonnet gravity, inspiraling black holes with opposite scalar charges can undergo a sudden charge-flip, changing scalar radiation from dipolar to quadrupolar and inducing orbital eccentricity.

  2. Towards long and accurate numerical relativity waveforms of binary black holes beyond general relativity

    gr-qc 2026-07 conditional novelty 6.5 of 10

    Spectral methods plus comoving fixing-the-equations drivers yield 40+ cycle equal-mass sGB binary waveforms with phase error ≲1 rad, distinguishable from GR and merging earlier.

  3. Higher-derivative gravitational effective field theories are generically weakly hyperbolic

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    Any pure-metric higher-derivative gravity EFT with derivative-independent characteristics has a weakly hyperbolic physical spin-2 block that gauge fixing and constraint addition cannot remove.

  4. High-accuracy drivers to simulate black hole binaries beyond general relativity with the fixing-the-equations approach

    gr-qc 2026-07 conditional novelty 6.0 of 10

    Comoving tensor-aware driver equations in SpECTRE yield ~40-cycle sGB binary waveforms with O(1) rad phase error and eccentricity ≲10^{-3}, free of spurious spin growth.

  5. Scalar fields from nonlinear sigma models on black hole spacetimes

    gr-qc 2025-08 conditional novelty 6.0 of 10

    Numerical evolutions show positive-curvature SL(2,R) sigma-model scalars create denser clouds and earlier binary mergers, while negative-curvature O(3) scalars spread out and delay mergers.

  6. Challenges in the nonlinear evolution of unequal mass binaries in sGB gravity

    gr-qc 2025-07 conditional novelty 6.0 of 10

    First full merger simulations of 2:1 and 3:1 black hole binaries in scalar-Gauss-Bonnet gravity, with weak-coupling dephasing matching PN predictions but strong-coupling results limited by initial-data transients.

  7. Inflaton Dynamics in Higher-Derivative Scalar-Tensor Theories of Gravity

    gr-qc 2025-05 conditional novelty 6.0 of 10

    In the weakly coupled regime of a four-derivative scalar-tensor theory, large inflationary inhomogeneities decay just as in general relativity, and only finely tuned initial data can escape the effective field theory'...

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