Geometric uniqueness for non-vacuum Einstein equations and applications

TL;DR

This paper demonstrates local geometric uniqueness for Einstein equations coupled with various matter models without regularity loss, extending previous vacuum results, and explores local regularity under geometric bounds.

Contribution

It extends the Planchon-Rodnianski uniqueness theorem to non-vacuum Einstein equations and investigates local regularity conditions for spacetimes.

Findings

Local geometric uniqueness holds without regularity loss for coupled Einstein-matter systems.

Extension of vacuum uniqueness theorem to a broad class of matter models.

Analysis of local regularity of spacetimes under geometric bounds.

Abstract

We prove in this note that local geometric uniqueness holds true without loss of regularity for Einstein equations coupled with a large class of matter models. We thus extend the Planchon-Rodnianski uniqueness theorem for vacuum spacetimes. In a second part of this note, we investigate the question of local regularity of spacetimes under geometric bounds.