Sufficient Conditions for Apparent Horizons in Spherically Symmetric Initial Data

Abstract

We establish sufficient conditions for the appearance of apparent horizons in spherically symmetric initial data when spacetime is foliated extrinsically. Let $M$ and $P$ be respectively the total material energy and the total material current contained in some ball of radius $\ell$. Suppose that the dominant energy condition is satisfied. We show that if $M-P\ge \ell$ then the region must possess a future apparent horizon for some non -trivial closed subset of such gauges. The same inequality holds on a larger subset of gauges but with a larger constant of proportionality which depends weakly on the gauge. This work extends substantially both our joint work on moment of time symmetry initial data as well as the work of Bizon, Malec and Ó Murchadha on a maximal slice.

16 pages, revtex, to appear in Phys. Rev. D

References in corpus (2)

• Necessary Conditions for Apparent Horizons and Singularities in Spherically Symmetric Initial Data
• Geometric Bounds in Spherically Symmetric General Relativity

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• The Hoop Conjecture in Spherically Symmetric Spacetimes
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• Necessary Conditions for Apparent Horizons and Singularities in Spherically Symmetric Initial Data
• Analytical studies on the hoop conjecture in charged curved spacetimes
• Towards a Supersymmetric Generalization of the Schwarzschild Black Hole
• Singularities in asymptotically anti-de Sitter spacetimes
• Geometric Bounds in Spherically Symmetric General Relativity
• Investigations on hoop conjecture for horizonless spherical charged stars
• A unified hoop conjecture for black holes and horizonless compact stars