Inhomogeneous space-time; its causal structure and possible fractal behaviour.

Details Inhomogeneous space-time; its causal structure and possible fractal behaviour. Inhomogeneous space-time; its causal structure and possible fractal behaviour.

Nov 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995ncimb.110.1277c&link_type=abstract

Nuovo Cimento B, Vol. 110B, No. 11, p. 1277 - 1285

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Universe: Space-Time

Scientific paper

Exact solutions are obtained for a higher-dimensional inhomogeneous space-time with dust as matter content. When the space-time becomes four, the model reduces to the well-known Tolman-Bondi solution. The shell-focusing singularity generally associated with this type of inhomogeneous collapse is discussed. It is observed that a 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 one obtains yet another counterexample of the cosmic-censorship conjecture. With suitable adjustment of the arbitrary functions of integration the space-time can be reduced to the zero-curvature Friedmann-like dust solution. It is further observed that the Friedmann-like solution does not appear to exhibit any fractal behaviour, which agrees with a similar conclusion made by Ribeiro (1992) in a recent communication.

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