  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 $K_{\rm min}$ 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 $K_{\rm min}$ is larger
than unity, then an apparent horizon must form, signalling the formation of a
black hole.
