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Cited by 260

The DOI matches its Crossref record; 105 of the 105 references it cites were found in a registry or an index.

A 3+1 perspective on null hypersurfaces and isolated horizons

Open access
Gourgoulhon, Eric, Jaramillo, José Luis·2006·Physics Reports
DOI 10.1016/j.physrep.2005.10.005
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Abstract

Abstract The isolated horizon formalism recently introduced by Ashtekar et al. aims at providing a quasi-local concept of a black hole in equilibrium in an otherwise possibly dynamical spacetime. In this formalism, a hierarchy of geometrical structures is constructed on a null hypersurface. On the other side, the 3 + 1 formulation of general relativity provides a powerful setting for studying the spacetime dynamics, in particular gravitational radiation from black hole systems. Here we revisit the kinematics and dynamics of null hypersurfaces by making use of some 3 + 1 slicing of spacetime. In particular, the additional structures induced on null hypersurfaces by the 3 + 1 slicing permit a natural extension to the full spacetime of geometrical quantities defined on the null hypersurface. This four-dimensional point of view facilitates the link between the null and spatial geometries. We proceed by reformulating the isolated horizon structure in this framework. We also reformulate previous works, such as Damour's black hole mechanics, and make the link with a previous 3 + 1 approach of black hole horizon, namely the membrane paradigm. We explicit all geometrical objects in terms of 3 + 1 quantities, putting a special emphasis on the conformal 3 + 1 formulation. This is in particular relevant for the initial data problem of black hole spacetimes for numerical relativity. Illustrative examples are provided by considering various slicings of Schwarzschild and Kerr spacetimes.

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Metadata

Authors
Gourgoulhon, E., & Jaramillo, J. L.
Venue
Physics Reports
Publisher
Elsevier BV
Published
2006-02
Volume
423
Issue
4-5
Pages
159-294
ISSN
0370-1573 (ISSN-L)
DOI
10.1016/j.physrep.2005.10.005
OpenAlex
W2099518530
Cited by
260
References
105
FWCI
6.29
Type
journal article
Language
en
Open access
green

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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

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