Gravitational Collapse of Vacuum Gravitational Field Configurations

Abstract

This paper proves a theorem about the existence of an apparent horizon in general relativity, which applies equally well to vacuum configurations and matter configurations. The theorem uses the reciprocal of the surface-to-volume ratio of a region on a space slice to measure the radius of the region, and uses the minimum value $K_{\min }$ of certain components of the extrinsic curvature to measure the strengh of the gravitational field in the region. The theorem proves that, if the product of the radius times $K_{\min }$ is larger than unity, then an apparent horizon must form, signalling the formation of a black hole.

arXiv comment10 pages and no figures, uses jnl macros (as at archive)

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