Marginally outer trap surface with capillary boundary and rigidity of initial data sets

TL;DR

This paper investigates the properties and rigidity of marginally outer trap surfaces with capillary boundaries in initial data sets, providing area estimates and extending results to higher dimensions using the Yamabe constant.

Contribution

It introduces new rigidity results for initial data sets with MOTS and capillary boundaries, including area estimates and high-dimensional extensions.

Findings

Established area estimates for MOTS with capillary boundary

Proved rigidity results for 3-dimensional initial data sets

Extended results to high dimensions using Yamabe constant

Abstract

In this paper, we present the several rigidity results of initial data sets with boundary when a marginally outer trap surface (MOTS) with capillary boundary is embedded. First, we establish estimates for the area of a MOTS with capillary boundary. Next, we prove a rigidity for 3-dimensional initial data sets with boundary. Furthermore, we extend our results from the 3-dimensional case to the high dimensional initial data sets using the Yamabe constant.