Numerical implementation of isolated horizon boundary conditions

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.Comment: 11 pages, 5 figures, references added and correcte

Inner boundary conditions for black hole Initial Data derived from Isolated Horizons

We present a set of boundary conditions for solving the elliptic equations in the Initial Data Problem for space-times containing a black hole, together with a number of constraints to be satisfied by the otherwise freely specifiable standard parameters of the Conformal Thin Sandwich formulation. These conditions altogether are sufficient for the construction of a horizon that is instantaneously in equilibrium in the sense of the Isolated Horizons formalism. We then investigate the application of these conditions to the Initial Data Problem of binary black holes and discuss the relation of our analysis with other proposals that exist in the literature.Comment: 13 pages. Major general revision. Section V comparing with previous approaches restructured; discussion on the lapse boundary condition extended. Appendix with some technical details added. Version accepted for publication in Phys.Rev.

The Dynamics of General Relativity

This article--summarizing the authors' then novel formulation of General Relativity--appeared as Chapter 7 of an often cited compendium edited by L. Witten in 1962, which is now long out of print. Intentionally unretouched, this posting is intended to provide contemporary accessibility to the flavor of the original ideas. Some typographical corrections have been made: footnote and page numbering have changed--but not section nor equation numbering etc. The authors' current institutional affiliations are encoded in: [email protected], [email protected], [email protected] .Comment: 30 pages (LaTeX2e), uses amsfonts, no figure

The Cauchy problem in General Relativity: An algebraic characterization

In this paper we shall analyse the structure of the Cauchy Problem (CP briefly) for General Relativity (GR briefly) by applying the theory of first order symmetric hyperbolic systems

Self-similar Bianchi models: I. Class A models

We present a study of Bianchi class A tilted cosmological models admitting a proper homothetic vector field together with the restrictions, both at the geometrical and dynamical level, imposed by the existence of the simply transitive similarity group. The general solution of the symmetry equations and the form of the homothetic vector field are given in terms of a set of arbitrary integration constants. We apply the geometrical results for tilted perfect fluids sources and give the general Bianchi II self-similar solution and the form of the similarity vector field. In addition we show that self-similar perfect fluid Bianchi VII$_0$ models and irrotational Bianchi VI$_0$ models do not exist.Comment: 14 pages, Latex; to appear in Classical and Quantum Gravit

Spherical Vesicles Distorted by a Grafted Latex Bead: An Exact Solution

We present an exact solution to the problem of the global shape description of a spherical vesicle distorted by a grafted latex bead. This solution is derived by treating the nonlinearity in bending elasticity through the (topological) Bogomol'nyi decomposition technique and elastic compatibility. We recover the ``hat-model'' approximation in the limit of a small latex bead and find that the region antipodal to the grafted latex bead flattens. We also derive the appropriate shape equation using the variational principle and relevant constraints.Comment: 12 pages, 2 figures, LaTeX2e+REVTeX+AmSLaTe