Recent results in mathematical relativity

TL;DR

This paper reviews recent advances in mathematical relativity, focusing on the global structure of vacuum Einstein solutions, including stability, cosmic censorship, and initial data construction.

Contribution

It provides a comprehensive overview of recent theoretical developments and new solution constructions in the field of mathematical relativity.

Findings

Enhanced understanding of asymptotic properties of solutions

New constructions of solutions with trapped surfaces

Progress in low regularity solutions

Abstract

We review selected recent results concerning the global structure of solutions of the vacuum Einstein equations. The topics covered include quasi-local mass, strong cosmic censorship, non-linear stability, new constructions of solutions of the constraint equations, improved understanding of asymptotic properties of the solutions, existence of solutions with low regularity, and construction of initial data with trapped surfaces or apparent horizons. This is an expanded version of a plenary lecture, sponsored by Classical and Quantum Gravity, held at the GR17 conference in Dublin in July 2004.