Hyperboloidal foliations and scri-fixing

TL;DR

This paper introduces a gauge choice using hyperboloidal foliations and scri-fixing to include null infinity in numerical simulations of test fields on asymptotically flat spacetimes, avoiding artificial boundaries.

Contribution

It explicitly constructs hyperboloidal coordinates with scri-fixing on Minkowski, Schwarzschild, and Kerr spacetimes, enabling more accurate numerical studies.

Findings

Inclusion of null infinity in computational domain.

Explicit construction of hyperboloidal coordinates on key spacetimes.

Avoidance of artificial outer boundaries in simulations.

Abstract

We discuss a gauge choice which allows us to avoid the introduction of artificial timelike outer boundaries in numerical studies of test fields based on a 3+1 decomposition of asymptotically flat background spacetimes. The main idea is to include null infinity in the computational domain by conformally compactifying the metric on hyperboloidal foliations and fixing the spatial coordinate location of null infinity, i.e. scri-fixing. We construct such coordinates explicitly on Minkowski, Schwarzschild and Kerr spacetimes.