Numerical implementation of isolated horizon boundary conditions

Abstract

We study the numerical implementation of a set of boundary conditions derived from the isolated horizon formalism, and which characterize a black hole whose horizon is in quasi-equilibrium. More precisely, we enforce these geometrical prescriptions as inner boundary conditions on an excised sphere, in the numerical resolution of the Conformal Thin Sandwich equations. As main results, we firstly establish the consistency of including in the set of boundary conditions a "constant surface gravity" prescription, interpretable as a lapse boundary condition, and secondly we assess how the prescriptions presented recently by Dain et al. for guaranteeing the well-posedness of the Conformal Transverse Traceless equations with quasi-equilibrium horizon conditions extend to the Conformal Thin Sandwich elliptic system. As a consequence of the latter analysis, we discuss the freedom of prescribing the expansion associated with the ingoing null normal at the horizon.

11 pages, 5 figures, references added and corrected

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• Spectral Methods for Numerical Relativity
• Improved constrained scheme for the Einstein equations: An approach to the uniqueness issue
• New theoretical approaches to black holes
• Mathematical Issues in a Fully-Constrained Formulation of Einstein Equations
• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
• The Einstein constraints: uniqueness and non-uniqueness in the conformal thin sandwich approach
• Beyond the Bowen-York extrinsic curvature for spinning black holes
• Construction of initial data for 3+1 numerical relativity
• Non-uniqueness in conformal formulations of the Einstein constraints
• An introduction to local Black Hole horizons in the 3+1 approach to General Relativity
• Excised black hole spacetimes: quasi-local horizon formalism applied to the Kerr example
• Trapping Horizons as inner boundary conditions for black hole spacetimes
• Excision boundary conditions for the conformal metric
• Isolated Horizon structures in quasiequilibrium black hole initial data
• An excision scheme for black holes in constrained evolution formulations: spherically symmetric case