Initial data and the end state of spherically symmetric gravitational collapse

Abstract

Generalizing earlier results on the initial data and the final fate of dust collapse, we study here the relevance of the initial state of a spherically symmetric matter cloud towards determining its end state in the course of a continuing gravitational collapse. It is shown that given an arbitrary regular distribution of matter at the initial epoch, there always exists an evolution from this initial data which would result either in a black hole or a naked singularity depending on the allowed choice of free functions available in the solution. It follows that given any initial density and pressure profiles for the cloud, there is a non-zero measure set of configurations leading either to black holes or naked singularities, subject to the usual energy conditions ensuring the positivity of energy density. We also characterize here wide new families of black hole solutions resulting from spherically symmetric collapse without requiring the cosmic censorship assumption.

Gravitational collapse: The story so far

“…In the following, using the general treatment given by Joshi and Dwivedi [7] we show that given an arbitrary regular distribution of a general matter field at the initial epoch, there always exists an evolution from this initial data which would result either in a black hole or a naked singularity, depending on the allowed choice of free functions available in the solution. It follows that either of these objects result depending on the nature of the regular initial data from which the collapse evolves.…”

“…Another important point that one has to consider is the matching of the gravitational collapse model above with a suitable exterior, which is either an asymptotically flat region, or a cosmological background. For details on this, as well as a discussion of energy conditions during the evolution of collapse, we refer to [7].…”

Strong curvature singularities in quasi-spherical asymptotically de Sitter dust collapse

“…A complete solution is given by equation (3), where R and ν are given by equations (4), (5) and (18), together with the energy density…”

Axially Symmetric Null Dust Space-Time, Naked Singularity, and Cosmic Time Machine

“…Papapetrou [17] pointed out the formation of naked singularities in Vaidya [18] radiating solution, a null dust fluid space-time generated from Schwarzschild vacuum solution. A small sample of spherically symmetric gravitational collapse solutions with a naked singularities are in [19][20][21][22][23][24][25][26][27][28][29][30]. Thus, the theoretical existence of naked singularities would mean that the gravitational collapse may be observable from the rest of the space-time.…”