Quasi-Spherical Gravitational Collapse in higher dimension and the effect of equation of state

Abstract

Gravitational collapse in (n+2) dimensional quasi-spherical space-time is studied for a fluid with non vanishing radial pressure. An exact analytic solution is obtained (ignoring the arbitrary integration function) for the equation of state $p_{r}=(\gamma-1)\rho.$ The singularity is studied locally by comparing the time of formation of apparent horizon and the central shell focusing singularity while the global nature of the final fate of collapse is characterized by the existence of radial null geodesic. It is revealed that the end state of collapse for D dimension with equation of state $p=-\rho$, for (D$-$1) dimensional dust and (D$-$2)dimension with equation of state $p=\rho$ are identical.