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Initial data and the end state of spherically symmetric gravitational collapse. (English) Zbl 0961.83032

This article is a continuation of [Classical Quantum Gravity 14, 1223-1236 (1997; Zbl 0873.53071)]. Summary: 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.

MSC:

83C75 Space-time singularities, cosmic censorship, etc.
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C57 Black holes

Citations:

Zbl 0873.53071
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