Nonlinear Evolution of Quadratic Gravity in 3+1 Dimensions

TL;DR

This paper develops a stable numerical framework for simulating quadratic gravity in 3+1 dimensions, demonstrating that it can behave similarly to General Relativity in vacuum scenarios despite known instabilities.

Contribution

It introduces a new stable evolution system for quadratic gravity and shows that it can replicate GR-like behavior in nonlinear vacuum evolutions.

Findings

Quadratic Gravity exhibits a known linear instability.

Ricci-flat solutions remain stable during evolution.

Black hole perturbations and mergers stay Ricci flat.

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.