The extended Conformal Einstein field equations with matter: the Einstein-Maxwell field

TL;DR

This paper extends conformal Einstein field equations to include trace-free matter such as electromagnetic fields, providing new gauges and proofs for the stability of Einstein-Maxwell spacetimes.

Contribution

It introduces a conformal gauge for Einstein-Maxwell equations that predicts the conformal boundary and proves stability results for related spacetimes.

Findings

New conformal gauge for Einstein-Maxwell equations

Proof of stability of Einstein-Maxwell de Sitter-like spacetimes

Semi-global stability of radiative Einstein-Maxwell spacetimes

Abstract

A discussion is given of the conformal Einstein field equations coupled with matter whose energy-momentum tensor is trace-free. These resulting equations are expressed in terms of a generic Weyl connection. The article shows how in the presence of matter it is possible to construct a conformal gauge which allows to know \emph{a priori} the location of the conformal boundary. In vacuum this gauge reduces to the so-called conformal Gaussian gauge. These ideas are applied to obtain: (i) a new proof of the stability of Einstein-Maxwell de Sitter-like spacetimes; (ii) a proof of the semi-global stability of purely radiative Einstein-Maxwell spacetimes.