Nonlinear Evolution of Quadratic Gravity in 3+1 Dimensions

Abstract

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.

18 pages (including 8 figures), with 6 appendices, references, and a supplementary file

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Cited by in corpus (14)

• The Science of the Einstein Telescope
• A non-Perturbative and Background-Independent Formulation of Quadratic Gravity
• Instability and backreaction of massive spin-2 fields around black holes
• Scalarization of isolated black holes in scalar Gauss-Bonnet theory in the fixing-the-equations approach
• Quasistationary hair for binary black hole initial data in scalar Gauss-Bonnet gravity
• Dust collapse and horizon formation in Quadratic Gravity
• Purely metric Horndeski theories and spontaneous curvaturization of black holes
• Gravitational collapse in Quadratic Gravity
• Conformal Cores of Quantum Black Holes in Quadratic Gravity
• Stable non-linear evolution in regularised higher derivative effective field theories
• Black holes and other exact solutions in six-derivative gravity
• Birkhoff's Theorem and Uniqueness: A Peek Beyond General Relativity
• Strict renormalizability as a paradigm for fundamental physics
• Mass gap in non-perturbative quadratic ${\mathcal{R}}^2$ gravity via Dyson-Schwinger