The Near-Linear Regime of Gravitational Waves in Numerical Relativity

TL;DR

This paper investigates a specific regime in numerical relativity where gravitational waves exhibit near-linear behavior but nonlinear effects can still cause instabilities, impacting the stability of Einstein equation simulations.

Contribution

It identifies and characterizes a near-linear regime of gravitational waves in 3D numerical relativity, highlighting potential instabilities in this parameter space.

Findings

Existence of a near-linear regime with low amplitude but nonlinear instabilities.

Nonlinearities can excite unstable modes in Einstein evolution equations.

Implications for stability and accuracy of numerical relativity simulations.

Abstract

We report on a systematic study of the dynamics of gravitational waves in full 3D numerical relativity. We find that there exists an interesting regime in the parameter space of the wave configurations: a near-linear regime in which the amplitude of the wave is low enough that one expects the geometric deviation from flat spacetime to be negligible, but nevertheless where nonlinearities can excite unstable modes of the Einstein evolution equations causing the metric functions to evolve out of control. The implications of this for numerical relativity are discussed.