The slicing dependence of non-spherically symmetric quasi-local horizons in Vaidya Spacetimes

Abstract

It is well known that quasi-local black hole horizons depend on the choice of a time coordinate in a spacetime. This has implications for notions such as the surface of the black hole and also on quasi-local physical quantities such as horizon measures of mass and angular momentum. In this paper, we compare different horizons on non-spherically symmetric slicings of Vaidya spacetimes. The spacetimes we investigate include both accreting and evaporating black holes. For some simple choices of the Vaidya mass function function corresponding to collapse of a hollow shell, we compare the area for the numerically found axisymmetric trapping horizons with the area of the spherically symmetric trapping horizon and event horizon. We find that as expected, both the location and area are dependent on the choice of foliation. However, the area variation is not large, of order $0.035\%$ for a slowly evolving horizon with $\dot{m}=0.02$. We also calculate analytically the difference in area between the spherically symmetric quasi-local horizon and event horizon for a slowly accreting black hole. We find that the difference can be many orders of magnitude larger than the Planck area for sufficiently large black holes.

arXiv comment10 pages, 5 figures, corrected minor typos

References in corpus (27)

• Formation and evaporation of non-singular black holes
• Isolated and dynamical horizons and their applications
• Comparison of post-Newtonian templates for compact binary inspiral signals in gravitational-wave detectors
• Matching post-Newtonian and numerical relativity waveforms: systematic errors and a new phenomenological model for non-precessing black hole binaries
• Inspiral, merger and ring-down of equal-mass black-hole binaries
• Black Hole Masses and Eddington Ratios at 0.3<z<4
• High-accuracy comparison of numerical relativity simulations with post-Newtonian expansions
• Dynamical Horizons and their Properties
• A Fast Apparent-Horizon Finder for 3-Dimensional Cartesian Grids in Numerical Relativity
• Black hole boundaries
• Local existence of dynamical and trapping horizons
• Where post-Newtonian and numerical-relativity waveforms meet
• Consistency of post-Newtonian waveforms with numerical relativity
• Finding Apparent Horizons in Numerical Relativity
• Comparisons of eccentric binary black hole simulations with post-Newtonian models
• Comparison of Numerical and Post-Newtonian Waveforms for Generic Precessing Black-Hole Binaries
• Isolated, slowly evolving, and dynamical trapping horizons: geometry and mechanics from surface deformations
• Non-symmetric trapped surfaces in the Schwarzschild and Vaidya spacetimes
• The Current Status of Binary Black Hole Simulations in Numerical Relativity
• Outer Trapped Surfaces in Vaidya Spacetimes
• Black holes and black hole thermodynamics without event horizons
• Area evolution, bulk viscosity and entropy principles for dynamical horizons
• A Note on trapped Surfaces in the Vaidya Solution
• The spatial relation between the event horizon and trapping horizon
• On the proximity of black hole horizons: lessons from Vaidya
• Where are the trapped surfaces?
• Involute, minimal, outer and increasingly trapped surfaces

Cited by in corpus (23)

• Tunnelling Methods and Hawking's radiation: achievements and prospects
• The region with trapped surfaces in spherical symmetry, its core, and their boundaries
• Trapped surfaces
• Spacetime near isolated and dynamical trapping horizons
• An introduction to local Black Hole horizons in the 3+1 approach to General Relativity
• Observational evidence for the formation of trapping horizons in astrophysical black holes
• Conformally rescaled spacetimes and Hawking radiation
• Quasi-local black hole horizons
• On the proximity of black hole horizons: lessons from Vaidya
• Tidal deformation of dynamical horizons in binary black hole mergers
• Marginally Trapped Surfaces in Spherical Gravitational Collapse
• Trapped surfaces in Oppenheimer-Snyder black holes
• Conformal Killing horizons and their thermodynamics
• Nonstationary regime for quasinormal modes of the charged Vaidya metric
• Symmetry and instability of marginally outer trapped surfaces
• Trapped region in Kerr-Vaidya space-time
• Survival of black holes through a cosmological bounce
• Conserved quantities for black hole solutions in pure Lovelock gravity
• Spherical trapped surfaces in n-dimensional general relativity
• Closest Safe Approach to an Accreting Black Hole
• Double null formulation of the general Vaidya metric
• Some examples of trapped surfaces
• Alternative characterization of a black hole boundary