General relativistic collapse of homothetic ideal gas spheres and planes.

Abstract

This paper presents in a succinct but self-contained style of our underatanding of the gravitational collapse of homothetic, ideal gas spheres and planes. The physical problem is reduced to a study of a nonlinear autonomous system of differential equations. It is first shown that this system is a Cauchy system everywhere in the projective space t/r ≡ ξ ∈ R. The concept of sonic Cauchy and apparent horizons is introduced, and it is shown that the set of globally analytic naked solutions is discrete as mentioned by Ori and Piran but is finite and even empty for very strong equations of state. Even when singularities may be «seen,» we are able to show that they cannot be «heard»