# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1705.09674