Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2000-10-09
Class.Quant.Grav. 18 (2001) 1651-1676
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Now 40pp. plain latex including 11 of figures (using pstricks.tex). Some proofs omitted for brevity (these are available in V1
Scientific paper
10.1088/0264-9381/18/9/304
A study is undertaken of the gravitational collapse of spherically symmetric thick shells admitting a homothetic Killing vector field under the assumption that the energy momentum tensor corresponds to the absence of a pure outgoing component of field. The energy-momentum tensor is not specified beyond this, but is assumed to satisfy the strong and dominant energy conditions. The metric tensor depends on only one function of the similarity variable and the energy conditions identify a class of functions ${\cal F}$ to which the metric function may belong. The possible global structure of such space-times is determined, with particular attention being paid to singularities and their temporal nature (naked or censored). It is shown that there are open subsets of ${\cal F}$ which correspond to naked singularities; in this sense, such singularities are stable. Furthermore, it is shown that these singularities can arise from regular (continuous), asymptotically flat initial data which deviate from the trivial data by an arbitrarily small amount.
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