Properties of Quasi-local mass in binary black hole mergers
arXiv:2308.10906 · doi:10.1103/PhysRevD.108.124031
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 (40)
- Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
- Evolution of Binary Black Hole Spacetimes
- Isolated and dynamical horizons and their applications
- The Einstein Toolkit: A Community Computational Infrastructure for Relativistic Astrophysics
- Gauge conditions for long-term numerical black hole evolutions without excision
- Dynamical Horizons and their Properties
- A single-domain spectral method for black hole puncture data
- Dynamical Horizons: Energy, Angular Momentum, Fluxes and Balance Laws
- Black hole boundaries
- A 3+1 perspective on null hypersurfaces and isolated horizons
- Local existence of dynamical and trapping horizons
- Turduckening black holes: an analytical and computational study
- Towards a Stable Numerical Evolution of Strongly Gravitating Systems in General Relativity: The Conformal Treatments
- Positivity of Quasilocal Mass
- Quasilocal mass in general relativity
- Isometric embeddings into the Minkowski space and new quasi-local mass
- Kranc: a Mathematica application to generate numerical codes for tensorial evolution equations
- Energy and entropy conservation for dynamical black holes
- The area of horizons and the trapped region
- Quasilocal Energy for a Kerr black hole
- 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
- A comment on Liu and Yau's positive quasi-local mass
- Conserved quantities in general relativity: from the quasi-local level to spatial infinity
- The interior of a binary black hole merger
- On geometric problems related to Brown-York and Liu-Yau quasilocal mass
- An introduction to local Black Hole horizons in the 3+1 approach to General Relativity
- The existence and stability of marginally trapped surfaces
- Self-intersecting marginally outer trapped surfaces
- 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
- Limit of quasilocal mass at spatial infinity
- Foliations by stable spheres with constant mean curvature for isolated systems without asymptotic symmetry
- Evolution of angular momentum and center of mass at null infinity
- Evaluating quasilocal energy and solving optimal embedding equation at null infinity
- Minimizing properties of critical points of quasi-local energy
- 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