Some rigidity results for compact initial data sets

TL;DR

This paper establishes new rigidity theorems for compact initial data sets in general relativity, extending previous results and providing illustrative examples under specific energy, boundary, and topological conditions.

Contribution

It introduces several new rigidity results for compact initial data sets, broadening the scope of earlier theorems and including boundary and topological considerations.

Findings

Global rigidity results under natural conditions

Extensions of previous rigidity theorems

Illustrative examples demonstrating the results

Abstract

In this paper, we prove several rigidity results for compact initial data sets, in both the boundary and no boundary cases. In particular, under natural energy, boundary, and topological conditions, we obtain a global version of the main result in [15]. We also obtain some extensions of results in [12]. A number of examples are given in order to illustrate some of the results presented in this paper.