Inhomogeneous space-time; Its causal structure and possible fractal behaviour

Abstract

Exact solutions are obtained for a higher-dimensional inhomogeneous space-time with dust as matter content. When the space-time becomes four, our model reduces to the well-known Tolman-Bondi solution. Shell-focussing singularity generally associated with this type of inhomogeneous collapse is discussed. It is observed that naked singularity appears if the degree of inhomogeneity exceeds a critical value, which is slightly larger than the corresponding value in the 4D case. Thus we obtain yet another counterexample of the cosmic-censorship conjecture. With suitable adjustment of the arbitrary functions of integration our space-time can be reduced to the zero-curvature Friedmann-like dust solution. It is further observed that our Friedmann-like solution does not appear to exhibit any fractal behaviour, which agrees with a similar conclusion made by Ribeiro in a recent communication.