The Geometry of Collapsing Isotropic Fluids

Abstract

The study of spherically symmetric spacetimes modeling collapsing isotropic fluids is a recurrent topic in relativistic literature. What makes it one of the most intriguing problems in gravitational collapse is that perfect fluids are a direct, physically interesting generalization of the so-called Tolman–Bondi–Lemaitre (TBL) solution, which is one of the few known-in-details solutions dynamically collapsing to a singularity. The TBL solution is indeed long known to have naked singularities, while the case of isotropic fluids remains almost open. Some results are actually known from numerical relativity, but little is known about the geometry of the spacetimes: whether a singularity is developed, and if that is the case, what is the causal structure of the solution. We report here on some recent results which shed new light on this problem.