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. Furthermore, this suggests that, at least in vacuum, classical quadratic gravity can mimic General Relativity, even in the fully nonlinear strong-gravity regime.