Black Hole Boundary Conditions and Coordinate Conditions
arXiv:gr-qc/9703027 · doi:10.1103/PhysRevD.57.2299
Abstract
This paper treats boundary conditions on black hole horizons for the full 3+1D Einstein equations. Following a number of authors, the apparent horizon is employed as the inner boundary on a space slice. It is emphasized that a further condition is necessary for the system to be well posed; the ``prescribed curvature conditions" are therefore proposed to complete the coordinate conditions at the black hole. These conditions lead to a system of two 2D elliptic differential equations on the inner boundary surface, which coexist nicely to the 3D equation for maximal slicing (or related slicing conditions). The overall 2D/3D system is argued to be well posed and globally well behaved. The importance of ``boundary conditions without boundary values" is emphasized. This paper is the first of a series. This revised version makes minor additions and corrections to the previous version.
13 pages LaTeX, revtex. No figures
Cited by in corpus (52)
- Isolated and dynamical horizons and their applications
- Black hole boundaries
- A 3+1 perspective on null hypersurfaces and isolated horizons
- Numerical Relativity: A review
- Introduction to dynamical horizons in numerical relativity
- Small localized black holes in a braneworld: Formulation and numerical method
- Solutions of the Einstein Constraint Equations with Apparent Horizon Boundaries
- Corotating and irrotational binary black holes in quasi-circular orbits
- A New Area Law in General Relativity
- Dynamical surface gravity
- Isolated, slowly evolving, and dynamical trapping horizons: geometry and mechanics from surface deformations
- The region with trapped surfaces in spherical symmetry, its core, and their boundaries
- Non-symmetric trapped surfaces in the Schwarzschild and Vaidya spacetimes
- Extremality conditions for isolated and dynamical horizons
- A generalized Damour-Navier-Stokes equation applied to trapping horizons
- Foliation dependence of black hole apparent horizons in spherical symmetry
- Outer Trapped Surfaces in Vaidya Spacetimes
- Trapped surfaces
- Black holes and black hole thermodynamics without event horizons
- Quasinormal modes and their overtones at the common horizon in a binary black hole merger
- From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
- Area evolution, bulk viscosity and entropy principles for dynamical horizons
- Moving Black Holes in 3D
- A Note on trapped Surfaces in the Vaidya Solution
- Asymptotically FRW black holes
- Algebra of diffeomorphism-invariant observables in Jackiw-Teitelboim Gravity
- Numerical Evolution of Black Holes with a Hyperbolic Formulation of General Relativity
- An introduction to local Black Hole horizons in the 3+1 approach to General Relativity
- Causal Nature and Dynamics of Trapping Horizons in Black Hole Collapse
- Euler-Plateau, with a twist
- Quasi-local black hole horizons
- Spacetimes containing slowly evolving horizons
- Numerical implementation of isolated horizon boundary conditions
- Fundamental properties and applications of quasi-local black hole horizons
- Trapping Horizons as inner boundary conditions for black hole spacetimes
- Isolated and dynamical horizons from a common perspective
- Quasi-Local Black Hole Horizons: Recent Advances
- Gravitational Collapse in the EGB Gravity
- A Young-Laplace law for black hole horizons
- Marginally Trapped Surfaces in Spherical Gravitational Collapse
- Trapped surfaces in Oppenheimer-Snyder black holes
- Trapped and marginally trapped surfaces in Weyl-distorted Schwarzschild solutions
- Where are the trapped surfaces?
- Fermionic edge states and new physics
- Black holes as local horizons
- Closed Universes With Black Holes But No Event Horizons As a Solution to the Black Hole Information Problem
- Two physical characteristics of numerical apparent horizons
- Evolving black hole horizons in General Relativity and alternative gravity
- Spherical trapped surfaces in n-dimensional general relativity
- Some uniqueness results for dynamical horizons
- Some examples of trapped surfaces
- A trapped surface in the higher-dimensional self-similar Vaidya spacetime