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General Relativity and Quantum Cosmology, gr-qc
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.
