Properties of Quasi-local mass in binary black hole mergers

TL;DR

This paper investigates the properties and behavior of the Wang-Yau quasi-local mass in numerical simulations of binary black hole mergers, highlighting its potential as a meaningful measure of energy in general relativity.

Contribution

It provides a detailed numerical analysis of the Wang-Yau quasi-local mass during black hole collisions, exploring its properties and evolution in full general relativity.

Findings

Wang-Yau mass behaves consistently with physical expectations during mergers

Comparison with irreducible mass reveals insightful differences

Mathematical subtleties are identified in defining mass for trapped surfaces

Abstract

Identifying a general quasi-local notion of energy-momentum and angular momentum would be an important advance in general relativity with potentially important consequences for mathematical and astrophysical studies in general relativity. In this paper we study a promising approach to this problem first proposed by Wang and Yau in 2009 based on isometric embeddings of closed surfaces in Minkowski space. We study the properties of the Wang-Yau quasi-local mass in high accuracy numerical simulations of the head-on collisions of two non-spinning black holes within full general relativity. We discuss the behavior of the Wang-Yau quasi-local mass on constant expansion surfaces and we compare its behavior with the irreducible mass. We investigate the time evolution of the Wang-Yau Quasi-local mass in numerical examples. In addition we discuss mathematical subtleties in defining the Wang-Yau mass for marginally trapped surfaces.