Solutions of the Einstein equations with matter

TL;DR

This paper surveys recent solutions to Einstein's equations with matter, covering asymptotically flat, spatially compact spacetimes, and their relation to other theories, highlighting open questions and future research directions.

Contribution

It provides a comprehensive overview of recent developments in Einstein-matter solutions and discusses potential methods for future studies.

Findings

Analysis of asymptotically flat solutions

Discussion of spatially compact solutions

Relevance of matter solutions to general relativity

Abstract

Recent results on solutions of the Einstein equations with matter are surveyed and a number of open questions are stated. The first group of results presented concern asymptotically flat spacetimes, both stationary and dynamical. Then there is a discussion of solutions of the equations describing matter in special relativity and Newtonian gravitational theory and their relevance for general relativity. Next spatially compact solutions of the Einstein-matter equations are presented. Finally some remarks are made on the methods which have been used, and could be used in the future, to study solutions of the Einstein equations with matter.