Spherical gravitational collapse inNdimensions

Abstract

We investigate here spherically symmetric gravitational collapse in a spacetime with an arbitrary number of dimensions and with a general type I matter field, which is a broad class that includes most of the physically reasonable matter forms. We show that given the initial data for matter in terms of the initial density and pressure profiles at an initial surface t = ti from which the collapse evolves, there exist rest of the initial data functions and classes of solutions of Einstein equations which we construct here, such that the spacetime evolution goes to a final state which is either a black hole or a naked singularity, depending on the nature of initial data and evolutions chosen, and subject to validity of the weak energy condition. The results are discussed and analyzed in the light of the cosmic censorship hypothesis in black hole physics. The formalism here combines the earlier results on gravitational collapse in four dimensions in a unified treatment. Also the earlier work is generalized to higher dimensional spacetimes to allow a study of the effect of number of dimensions on the possible final outcome of the collapse in terms of either a black hole or naked singularity. No restriction is adopted on the number of dimensions, and other limiting assumptions such as self-similarity of spacetime are avoided, in order to keep the treatment general. Our methodology allows to consider to an extent the genericity and stability aspects related to the occurrence of naked singularities in gravitational collapse.

Spacetime Singularities

“…A consideration to a general form of matter was given by Lake (1992); and by Szekeres and Iyer (1993), who do not start by assuming an equation of state but a class of metric coefficients is considered with a certain power law behavior. Also, Joshi and Dwivedi (1999) and Goswami and Joshi (2007), gave results in this direction. The main argument is along the following lines.…”

Cosmic censorship conjecture revisited: covariantly

“…Although no conclusive proof or disproof of CCC could be formulated, the quest gave rise to a number of counter examples which showed there are shell focusing naked singularities occurring at the centre of spherically symmetric dust, perfect fluids or radiation shells (see for example [3,4] and the references therein). We can, in principle, rule out these naked singularities by stating that dust or perfect fluids are not really 'fundamental' forms of matter field, as their properties are not derived from a 'proper' Lagrangian.…”

M-theory branes: U-duality properties and a class of new static solutions

“…In the context of four dimensional JNWW solutions, such collapse processes and various issues involving naked singularities have been extensively studied in [14,16]. Similar studies are also needed in the present context.…”