Pramana | |
Stability of naked singularity arising in gravitational collapse of Type I matter fields | |
R V Saraykar22  Sanjay B Sarwe11  | |
[1] Department of Mathematics, S.F.S. College, Seminary Hill, Nagpur 440 006, India$$;Department of Mathematics, Nagpur University Campus, Nagpur 440 033, India$$ | |
关键词: Gravitational collapse; central-singularity; stability.; | |
DOI : | |
学科分类:物理(综合) | |
来源: Indian Academy of Sciences | |
【 摘 要 】
Considering gravitational collapse of Type I matter fields, we prove that, given an arbitrary ð¶2-mass function ð‘€(ð‘Ÿ, ð‘£) and a ð¶1-function â„Ž(ð‘Ÿ, ð‘£) (through the corresponding ð¶1-metric function ðœˆ(ð‘¡, ð‘Ÿ)), there exist infinitely many choices of energy distribution function ð‘(ð‘Ÿ) such that the `true’ initial data (ð‘€, â„Ž(ð‘Ÿ, ð‘£)) 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 (BH) and naked singularity (NS) 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 ð‘ð‘Ÿ(ð‘Ÿ) has been illustrated in details to get a clear picture of how naked singularity is formed and how, it is stable with respect to initial data.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
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RO201912040496889ZK.pdf | 231KB | download |