Stability of Naked Singularity arising in gravitational collapse of Type I matter fields

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dc.creatorSarwe, Sanjay B.
dc.creatorSaraykar, R. V.
dc.date2003-10-22
dc.date2004-10-06
dc.date.accessioned2026-07-07T11:08:42Z
dc.date.available2026-07-07T11:08:42Z
dc.descriptionConsidering gravitational collapse of Type I matter fields, we prove that, given an arbitrary $C^{2}$- mass function $\textit{M}(r,v)$ and a $C^{1}$- function $h(r,v)$ (through the corresponding $C^{1}$- metric function $ν(t,r)$), there exist infinitely many choices of energy distribution function $b(r)$ such that the `true' initial data ($\textit{M},h(r,v)$) leads the collapse to the formation of naked singularity. We further prove that the occurrence of such a naked singularity is stable with respect to small changes in the initial data. We remark that though the initial data leading to both black hole and naked singularity form a "big" subset of the true initial data set, their occurrence is not generic. The terms `stability' and `genericity' are appropriately defined following the theory of dynamical systems. The particular case of radial pressure $p_{r}(r)$ has been illustrated in details to get clear picture of how naked singularity is formed and how, it is stable with respect to initial data.
dc.description16 pages, no figure, Latex, submitted to Pramana
dc.identifierhttps://arxiv.org/abs/gr-qc/0310106
dc.identifierhttp://arxiv.org/abs/gr-qc/0310106
dc.identifierPramana65:17-33,2005
dc.identifierdoi:10.1007/BF02704372
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/190222
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleStability of Naked Singularity arising in gravitational collapse of Type I matter fields
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