Nonlinear wave equations for numerical relativity: towards the computation of gravitational wave forms of black hole binaries

TL;DR

This paper introduces a new covariant, hyperbolic formulation for numerical relativity to improve the simulation of gravitational waves from black hole binaries, especially in the late inspiral stages.

Contribution

It presents a fully covariant, strictly hyperbolic formulation for numerical relativity that enables flexible foliations without restrictions on the lapse function.

Findings

Successfully demonstrated in a 1D Gowdy-wave simulation

Allows general foliations, enhancing simulation flexibility

Potential to improve gravitational wave predictions from binary mergers

Abstract

The prime candidate of LIGO/VIRGO sources of gravitational waves is the spiral in of black holes and neutron stars in compact binaries. While the early stages of the evolution of compact binaries is computable from post-Newtonian calculations, prediction of their late stages requires large scale numerical simulation. A fully covariant and strictly hyperbolic formulation for numerical relativity is described, and illustrated in a one-dimensional computation of a Gowdy-wave on the three-torus. This formulation allows foliations in full generality, in particular it poses no restriction on the lapse function.