New Formalism for Numerical Relativity

TL;DR

This paper introduces a new first-order, flux-conservative hyperbolic formulation of Einstein's equations, enabling the application of advanced numerical methods in numerical relativity across various slicing conditions.

Contribution

It presents a novel formulation of Einstein's equations that is compatible with a wide range of slicing conditions, facilitating improved numerical simulations.

Findings

Formulation is explicitly first order and flux-conservative

Applicable to a broad class of slicing conditions including maximal slicing

Enables use of advanced numerical methods from fluid dynamics

Abstract

We present a new formulation of the Einstein equations that casts them in an explicitly first order, flux-conservative, hyperbolic form. We show that this now can be done for a wide class of time slicing conditions, including maximal slicing, making it potentially very useful for numerical relativity. This development permits the application to the Einstein equations of advanced numerical methods developed to solve the fluid dynamic equations, {\em without} overly restricting the time slicing, for the first time. The full set of characteristic fields and speeds is explicitly given.