Higher dimensional radiation collapse and cosmic censorship

Abstract

We study the occurrence of naked singularities in the spherically symmetric collapse of radiation shells in a higher dimensional spacetime. The necessary conditions for the formation of a naked singularity or a black hole are obtained. The naked singularities are found to be strong in the Tipler's sense and thus violating cosmic censorship conjecture.PACS numbers: 04.20.DwThe cosmic censorship conjecture (CCC) put forward some three decades ago by Penrose [1] says that in generic situation all singularities arising from regular initial data are clothed by event horizon. Since CCC remains as an unresolved issue in classical general relativity, examples which appear to violate conjecture remain important and may be valuable when one attempts to formulate notion of CCC in concrete mathematical form. The Vaidya solution [2] is most commonly used as a testing ground for various forms of the CCC. In particular, Papapetrou [3] first showed that this solution can give rise to the formation of naked singularities and thus provided one of the earlier counter examples to CCC. Since then, the solution is extensively studied in gravitational collapse with reference to CCC (see e.g. [4] and references therein). Lately, there has been interest in studying gravitational collapse in higher dimensions [5]. This brief report searches for the occurrence of naked singularities in higher dimensional Vaidya spacetime and if they do, to investigate whether the dimensionality of spacetime has any role in the nature of singularities. We find that higher dimensional Vaidya spacetime admit strong-curvature naked singularities in the Tipler's [6] sense.The idea that spacetime should be extended from four to higher dimensions was introduced by Kaluza and Klein [7] to unify gravity and electromagnetism. Five dimensional (5D) spacetime is particularly more relevant because both 10D and 11D super-gravity theories yield solutions where a 5D spacetime results after dimensional reduction [8]. Hence, we shall confine ourselves to 5D case. It should be noted that higher dimensional spacetimes where all dimensions are in the equal foot, like ones to be considered here, are not so realistic, as we are living in effectively 4-dimensional spacetime. So in principle one might expect that by dimensional reduction the higher dimensional spacetime should reduce to our 4-dimensional world. In this sense, the models considered in this paper are ideal. * Electronic address: sgghosh@yahoo.com † Electronic address: sarayaka@nagpur.dot.net.inThe metric of collapsing Vaidya models in 5D case is [9]where v is null coordinate which represents advanced Eddington time with −∞ < v < ∞, r is radial coordinate with 0 ≤ r < ∞, dΩ 2 = dθ 2 1 + sin 2 θ 1 (dθ 2 2 + sin 2 θ 2 dθ 2 3 ) is a metric of 3 sphere and the arbitrary function m(v) (which is restricted only by the energy conditions), represents the mass at advanced time v. The energy momentum tensor can be written in the formwith the null vector k a satisfying k a = −δ v a and k a k a = 0. We have used the units whi...

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