Hyperboloidal evolution with the Einstein equations

TL;DR

This paper presents a method for hyperboloidal evolution in Einstein equations that allows null infinity to be fixed independently of time, improving numerical relativity techniques for wave extraction and boundary handling.

Contribution

It introduces a freely prescribable conformal scale factor and a gauge choice that regularizes the equations at null infinity, enhancing the well-posedness of hyperboloidal initial value problems.

Findings

Null infinity location can be fixed independently of time.

Conformal source terms become regular at null infinity.

Method benefits numerical relativity for wave extraction.

Abstract

We consider an approach to the hyperboloidal evolution problem based on the Einstein equations written for a rescaled metric. It is shown that a conformal scale factor can be freely prescribed a priori in terms of coordinates in a well-posed hyperboloidal initial value problem such that the location of null infinity is independent of the time coordinate. With an appropriate choice of a single gauge source function each of the formally singular conformal source terms in the equations attains a regular limit at null infinity. The suggested approach could be beneficial in numerical relativity for both wave extraction and outer boundary treatment.