Two physical characteristics of numerical apparent horizons

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چکیده

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Two physical characteristics of numerical apparent horizons

This article translates some recent results on quasilocal horizons into the language of (3 + 1) general relativity so as to make them more useful to numerical relativists. In particular quantities are described which characterize how quickly an apparent horizon is evolving and how close it is to either equilibrium or extremality.

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We review various algorithms for finding apparent horizons in 3+1 numerical relativity. We then focus on one particular algorithm, in which we pose the apparent horizon equation H ≡ ∇in + Kijnn − K = 0 as a nonlinear elliptic (boundary-value) PDE on angular-coordinate space for the horizon shape function r = h(θ, φ), finite difference this PDE, and use Newton’s method or a variant to solve the ...

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Finding apparent horizons and other two-surfaces of constant expansion

Apparent horizons are structures of spacelike hypersurfaces that can be determined locally in time. Closed surfaces of constant expansion (CE surfaces) are a generalisation 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 ...

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Event horizons and apparent horizons in spherically symmetric geometries.

Spherical configurations that are very massive must be surrounded by apparent horizons. These in turn, when placed outside a collapsing body, have a fixed area and must propagate outward with a velocity equal to the velocity of radially outgoing photons. That proves, within the framework of the (1+3) formalism and without resorting to the Birkhoff theorem, that apparent horizons coincide with e...

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ژورنال

عنوان ژورنال: Canadian Journal of Physics

سال: 2008

ISSN: 0008-4204,1208-6045

DOI: 10.1139/p07-194