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arXiv · 2308.10906

Properties of Quasi-local mass in binary black hole mergers

Daniel Pook-Kolb·Bowen Zhao·Lars Andersson·Badri Krishnan·Shing-Tung Yau
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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.

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Daniel Pook-Kolb, Bowen Zhao, Lars Andersson, Badri Krishnan, Shing-Tung Yau. 2023-08-19. Properties of Quasi-local mass in binary black hole mergers. https://doi.org/10.1103/physrevd.108.124031

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