GRAVITATIONAL COLLAPSE OF AN INHOMOGENEOUS DUST SPHERE IN HIGHER-DIMENSIONAL SPACETIME

A class of interior solutions for a spherically inhomogeneous dust dis tribution in multidimensional space-time is obtained. This generalizes to (n + 2)-dimension, the well-known solution of Tolman-Bondi in the sense that when n = 2 one recovers the Tolman-Bondi spacetime. The dyn amical behavior of the model is studied, and it is observed that there are some differences from the analogous four-dimensional case. Unlike the standard four-dimensional case where, in general, the metric coef ficients are obtained in parametric forms only, we here get the integr als of the field equations in closed form. Two important aspects, shel l crossing and shell focusing singularities which are generally associ ated with this type of inhomogeneous dust collapse, are also discussed . It is found that depending on the degree of inhomogeneity of the col lapsing matter it may, in some cases, lead to a naked singularity. Thi s offers counterexamples to the cosmic censorship hypothesis. A metric in the empty space which is continuous with the line element in a non comoving coordinate system in the interior is also presented. Under su itable transformations, our spacetime also reduces to the higher dimen sional analog of the Einstein-de Sitter model. It is further observed that a recollapsing inhomogeneous model may admit of spaces that are n ot closed (not finite in spatial extent).