Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-03-24
Phys. Rev. D 80, 024001 (2009)
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Version published in PRD
Scientific paper
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.
Kawakami Hayato
Mitsuda Eiji
Nambu Yasusada
Tomimatsu Akira
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