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Finding apparent horizons and other 2-surfaces of constant expansion

Erik Schnetter

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Apparent horizons are structures of spacelike hypersurfaces that can be determined locally in time. Closed surfaces of constant expansion (CE surfaces) are a generalization of apparent horizons. I present an efficient method for locating CE surfaces. This method uses an explicit representation of the surface, allowing for arbitrary resolutions and, in principle, shapes. The CE surface equation is then solved as a nonlinear elliptic equation. It is reasonable to assume that CE surfaces foliate a spacelike hypersurface outside an interior region, thus defining an invariant (but still slicing-dependent) radial coordinate. This can be used to determine gauge modes and compare time evolutions with different gauge conditions. CE surfaces also provide an efficient way of finding new apparent horizons as they appear, for example, in binary black hole simulations.


PACS

04.20.-q Classical general relativity

04.70.-s Physics of black holes

04.25.D- Numerical relativity

MSC

14Q10 Surfaces, hypersurfaces

35J30 General theory of higher-order, elliptic equations (See also 31A30, 31B30)

83C57 Black holes

Subjects

Gravitation and cosmology

Dates

Issue 22 (21 November 2003)

Received 3 June 2003

Published 3 October 2003



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