Sufficient Conditions for Apparent Horizons in Spherically Symmetric Initial Data

Details Sufficient Conditions for Apparent Horizons in Spherically Symmetric Initial Data Sufficient Conditions for Apparent Horizons in Spherically Symmetric Initial Data

1997-09-24

arxiv.org/abs/gr-qc/9709066v1

Phys.Rev. D56 (1997) 7658-7665

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

10.1103/PhysRevD.56.7658

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 \'O Murchadha on a maximal slice.

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