The Asymptotically Self-Similar Regime for the Einstein Vacuum Equations

TL;DR

This paper develops a local theory for constructing and classifying singular spacetimes that become asymptotically self-similar near singularities, extending to all spacetime dimensions and connecting with Fefferman-Graham's ambient metric.

Contribution

It introduces a new local framework for constructing and classifying asymptotically self-similar singular spacetimes in all dimensions, linking to existing formal asymptotic expansions.

Findings

Construction of singular spacetimes with asymptotic self-similarity

Classification of exact self-similar solutions

Connection to Fefferman-Graham ambient metric expansions

Abstract

We develop a local theory for the construction of singular spacetimes in all spacetime dimensions which become asymptotically self-similar as the singularity is approached. The techniques developed also allow us to construct and classify exact self-similar solutions which correspond to the formal asymptotic expansions of Fefferman and Graham's ambient metric.