A. Banerjee et al., GRAVITATIONAL COLLAPSE OF AN INHOMOGENEOUS DUST SPHERE IN HIGHER-DIMENSIONAL SPACETIME, The Astrophysical journal, 422(2), 1994, pp. 681-687
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).