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arXiv · 0903.4041

Asymptotic behavior of dynamical variables and naked singularity formation in spherically symmetric gravitational collapse

Hayato Kawakami·Eiji Mitsuda·Yasusada Nambu·Akira Tomimatsu
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Abstract

Considering gravitational collapse of matter, it is important problem to clarify what kind of conditions leads to the formation of naked singularity. For this purpose, we apply the 1+3 orthonormal frame formalism introduced by Uggla \textit{et al.} to spherically symmetric gravitational collapse of perfect fluid. This formalism allows us to construct an autonomous system of evolution and constraint equations for scale-invariant dynamical variables normalized by the volume expansion rate of the timelike orthonormal frame vector. We investigate the asymptotic evolution of such dynamical variables towards the formation of a central singularity and present a conjecture that the steep spatial gradient for the normalized density function is a characteristic of the naked singularity formation.

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Hayato Kawakami, Eiji Mitsuda, Yasusada Nambu, Akira Tomimatsu. 2009-03-24. Asymptotic behavior of dynamical variables and naked singularity formation in spherically symmetric gravitational collapse. https://doi.org/10.1103/physrevd.80.024001

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