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Nonlinear Evolution of Quadratic Gravity in 3+1 Dimensions

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arxiv 2306.04725 v1 pith:H4U36PIP submitted 2023-06-07 gr-qc

Aaron Held , Hyun Lim This is my paper · ORCID
classification gr-qc
keywords evolutiongravityquadraticnonlinearequationsgeneralinstabilityrelativity
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We present a numerically stable system of (3+1) evolution equations for the nonlinear gravitational dynamics of quadratic-curvature corrections to General Relativity (Quadratic Gravity). We also report on the numerical implementation of these evolution equations. We recover a well-known linear instability and gather evidence that -- aside from said instability -- Quadratic Gravity exhibits a physically stable Ricci-flat subsector. In particular, we demonstrate that Teukolsky-wave perturbations of a Schwarzschild black hole as well as a full binary inspiral (evolved up to merger) remain Ricci flat throughout evolution. This suggests that, at least in vacuum, classical Quadratic Gravity can mimic General Relativity, even in the fully nonlinear strong-gravity regime.

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Cited by 5 Pith papers

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

  1. Spherically symmetric solutions in quasi-local Einstein-Weyl gravity

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    In quasi-local Einstein-Weyl gravity, static spherically symmetric Frobenius solutions are classified: regular cores only, Schwarzschild-like horizons and wormhole throats, plus asymptotic 1/r^6 corrections to Schwarzschild.

  2. 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.

  3. 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.

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

    gr-qc 2026-07 conditional novelty 6.5 of 10

    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.

  5. 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.

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