Matching characteristic codes: exploiting two directions

TL;DR

This paper explores a method to combine incoming and outgoing characteristic formulations in numerical relativity, enabling better exploitation of spacetime causality and access to null infinity and interior regions, demonstrated in a 1D Einstein-Klein-Gordon model.

Contribution

It introduces a novel approach to combine characteristic formulations that enhances the numerical treatment of Einstein's equations in relativity simulations.

Findings

Effective combination of characteristic directions demonstrated in 1D model

Improved access to null infinity and interior regions in simulations

Potential for more accurate and causal numerical relativity computations

Abstract

Combining incoming and outgoing characteristic formulations can provide numerical relativists with a natural implementation of Einstein's equations that better exploits the causal properties of the spacetime and gives access to both null infinity and the interior region simultaneously (assuming the foliation is free of caustics and crossovers). We discuss how this combination can be performed and illustrate its behavior in the Einstein-Klein-Gordon field in 1D.