Rigidity of anti-de Sitter (2+1)-spacetimes with convex boundary near the Fuchsian locus

TL;DR

This paper proves that certain anti-de Sitter (2+1)-spacetimes with convex boundary near the Fuchsian locus are uniquely determined by the boundary metric, highlighting a rigidity property in this geometric setting.

Contribution

It establishes a rigidity theorem for globally hyperbolic compact anti-de Sitter spacetimes with convex boundary near the Fuchsian locus, based on boundary data.

Findings

Spacetimes are determined by boundary metric when holonomy is close to Fuchsian.

Rigidity holds for smooth or polyhedral convex boundaries.

Results extend understanding of geometric structures in anti-de Sitter spacetimes.

Abstract

We prove that globally hyperbolic compact anti-de Sitter (2+1)-spacetimes with strictly convex spacelike boundary that is either smooth or polyhedral and whose holonomy is close to Fuchsian are determined by the induced metric on the boundary.