A 3+1 perspective on null hypersurfaces and isolated horizons
By E. Gourgoulhon, J. Jaramillo. 2005
271 citations recorded by the source corpus.
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.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/584362684bcd5396a3081db4481d5bbe32bfec9a
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In Astronomy and Astrophysics
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In Nuclear and High Energy Physics
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- V. Lysov
- Venkat Chandrasekaran
- E. Flanagan
- Kartik Prabhu
- Irene Bredberg
- Cynthia Keeler
- Sabrina Pasterski
Citations in the corpus
- From Navier-Stokes to Einstein (2011, background): “In particular, excitations of a black hole horizon dissipate very much like those of a fluid [3–5, 12, 13, 28, 33–35], and there has been recent discussion of a holographic duality relating black holes and fluids [1, 8–10, 12, 14–17, 19, 21, 23, 24].”
- Symmetries and charges of general relativity at null boundaries (2018, background): “In this section we review the local geometry of null hypersurfaces [57, 58], in order to fix our notations and conventions.”