A stability result for purely radiative spacetimes

TL;DR

This paper proves an existence and stability result for a class of vacuum spacetimes with gravitational radiation, extending previous results from Minkowski spacetime to more general radiative cases using conformal methods.

Contribution

It generalizes semiglobal existence results to include spacetimes with gravitational radiation using conformal field equations and geodesic-based gauge.

Findings

Established stability of purely radiative vacuum spacetimes

Extended conformal field equations facilitate analysis of conformal boundary

Results applicable to spacetimes with gravitational radiation

Abstract

An existence and stability result for a class of purely radiative vacuum spacetimes arising from hyperboloidal data is given. This result generalises semiglobal existence results for Minkowski-like spacetimes to the case where the reference solution contains gravitational radiation. The analysis makes use of the extended conformal field equations and a gauge based on conformal geodesics so that the location and structure of the conformal boundary of the perturbed solutions is known a priori.