Properties of Quasi-local mass in binary black hole mergers

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.

References in corpus (12)

• Quasilocal mass in general relativity
• Isometric embeddings into the Minkowski space and new quasi-local mass
• The area of horizons and the trapped region
• Quasinormal modes and their overtones at the common horizon in a binary black hole merger
• Area evolution, bulk viscosity and entropy principles for dynamical horizons
• A Reformulation of the Hoop Conjecture
• What Happens to Apparent Horizons in a Binary Black Hole Merger?
• Self-Renormalization of the Classical Quasilocal Energy
• Ultimate fate of apparent horizons during a binary black hole merger II: Horizons weaving back and forth in time
• Evolution of angular momentum and center of mass at null infinity
• On the Hoop conjecture and the weak cosmic censorship conjecture for the axisymmetric Einstein-Vlasov system
• The Kijowski--Liu--Yau quasi-local mass of the Kerr black hole horizon

Cited by in corpus (2)

• Some Remarks on Wang-Yau Quasi-Local Mass
• Strong field behavior of Wang-Yau Quasi-local energy