Curvature conditions for the occurrence of a class of spacetime singularities

Details Curvature conditions for the occurrence of a class of spacetime singularities Curvature conditions for the occurrence of a class of spacetime singularities

1999-04-15

arxiv.org/abs/gr-qc/9904038v1

J. Math. Phys. 40 (1999) 3084-3090

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

RevTeX, 6 pages, no figures. To be published in J. Math. Phys

Scientific paper

10.1063/1.532746

It has previously been shown [W. Rudnicki, Phys. Lett. A 224, 45 (1996)] that a generic gravitational collapse cannot result in a naked singularity accompanied by closed timelike curves. An important role in this result plays the so-called inextendibility condition, which is required to hold for certain incomplete null geodesics. In this paper, a theorem is proved that establishes some relations between the inextendibility condition and the rate of growth of the Ricci curvature along incomplete null geodesics. This theorem shows that the inextendibility condition may hold for a much more general class of singularities than only those of the strong curvature type. It is also argued that some earlier cosmic censorship results obtained for strong curvature singularities can be extended to singularities corresponding to the inextendibility condition.

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