Nakedness and curvature strength of shell-focusing singularity in the spherically symmetric space-time with vanishing radial pressure

Details Nakedness and curvature strength of shell-focusing singularity in the spherically symmetric space-time with vanishing radial pressure Nakedness and curvature strength of shell-focusing singularity in the spherically symmetric space-time with vanishing radial pressure

1999-04-28

arxiv.org/abs/gr-qc/9904073v2

Class.Quant.Grav. 16 (1999) 2785-2796

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages, Accepted for Publication in Classical and Quantum Gravity, References Updated, Grammatical Errors Corrected

Scientific paper

10.1088/0264-9381/16/8/315

It was recently shown that the metric functions which describe a spherically symmetric space-time with vanishing radial pressure can be explicitly integrated. We investigate the nakedness and curvature strength of the shell-focusing singularity in that space-time. If the singularity is naked, the relation between the circumferential radius and the Misner-Sharp mass is given by $R\approx 2y_{0} m^{\beta}$ with $ 1/3<\beta\le 1$ along the first radial null geodesic from the singularity. The $\beta$ is closely related to the curvature strength of the naked singularity. For example, for the outgoing or ingoing null geodesic, if the strong curvature condition (SCC) by Tipler holds, then $\beta$ must be equal to 1. We define the ``gravity dominance condition'' (GDC) for a geodesic. If GDC is satisfied for the null geodesic, both SCC and the limiting focusing condition (LFC) by Kr\'olak hold for $\beta=1$ and $y_{0}\ne 1$, not SCC but only LFC holds for $1/2\le \beta <1$, and neither holds for $1/3<\beta <1/2$, for the null geodesic. On the other hand, if GDC is satisfied for the timelike geodesic $r=0$, both SCC and LFC are satisfied for the timelike geodesic, irrespective of the value of $\beta$. Several examples are also discussed.

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