Trapping Horizons as inner boundary conditions for black hole spacetimes

Abstract

We present a set of inner boundary conditions for the numerical construction of dynamical black hole space-times, when employing a 3+1 constrained evolution scheme and an excision technique. These inner boundary conditions are heuristically motivated by the dynamical trapping horizon framework and are enforced in an elliptic subsystem of the full Einstein equation. In the stationary limit they reduce to existing isolated horizon boundary conditions. A characteristic analysis completes the discussion of inner boundary conditions for the radiative modes.

arXiv comment4 pages, no figures, RevTeX4

References in corpus (22)

• Isolated and dynamical horizons and their applications
• General Laws of Black-Hole Dynamics
• Dynamical Horizons and their Properties
• Conformal ``thin sandwich'' data for the initial-value problem of general relativity
• 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
• Extrinsic Curvature and the Einstein Constraints
• Solving Einstein's Equations With Dual Coordinate Frames
• Excision boundary conditions for black hole initial data
• A constrained scheme for Einstein equations based on Dirac gauge and spherical coordinates
• Corotating and irrotational binary black holes in quasi-circular orbits
• Isolated, slowly evolving, and dynamical trapping horizons: geometry and mechanics from surface deformations
• Energy and entropy conservation for dynamical black holes
• Energy conservation for dynamical black holes
• Black Hole Boundary Conditions and Coordinate Conditions
• Area evolution, bulk viscosity and entropy principles for dynamical horizons
• Angular momentum conservation for dynamical black holes
• Inner boundary conditions for black hole Initial Data derived from Isolated Horizons
• On the existence of initial data containing isolated black holes
• Numerical implementation of isolated horizon boundary conditions

Cited by in corpus (13)

• New theoretical approaches to black holes
• Mathematical Issues in a Fully-Constrained Formulation of Einstein Equations
• Black holes and black hole thermodynamics without event horizons
• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
• An introduction to local Black Hole horizons in the 3+1 approach to General Relativity
• Constraint equations for general hypersurfaces and applications to shells
• Geometrical inequalities bounding angular momentum and charges in General Relativity
• Gravitational waves in dynamical spacetimes with matter content in the Fully Constrained Formulation
• Fundamental properties and applications of quasi-local black hole horizons
• Excised black hole spacetimes: quasi-local horizon formalism applied to the Kerr example
• Excision boundary conditions for the conformal metric
• An excision scheme for black holes in constrained evolution formulations: spherically symmetric case
• A Black-Hole Excision Scheme for General Relativistic Core-Collapse Supernova Simulations