Quasi-local mass and isometric embedding with reference to a static spacetime

TL;DR

This paper explores the application of isometric embedding techniques to define and analyze quasilocal mass in various static spacetimes within general relativity, including cosmological and black hole models.

Contribution

It introduces new methods for studying quasilocal mass using isometric embedding in static spacetimes, advancing the mathematical understanding in this area.

Findings

Progress in defining quasilocal mass in de Sitter and Anti-de Sitter spacetimes

Application of isometric embedding to Schwarzschild black hole spacetime

Development of mathematical tools linking geometry and mass in general relativity

Abstract

The mathematical theory of isometric embedding is applied to study the notion of quasilocal mass in general relativity. In particular, I shall report some recent progress of quasilocal mass with reference to a cosmological spacetime, such as the de Sitter or the Anti-de Sitter spacetime, or a blackhole spacetime, such as the Schwarzschild spacetime. This article is based on joint work with Po-Ning Chen, Ye-Kai Wang, and Shing-Tung Yau.