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

TL;DR

This paper analyzes gravitational collapse in higher-dimensional quasi-spherical spacetime with a fluid having radial pressure, deriving exact solutions and studying the nature of singularities and horizons.

Contribution

It provides an exact analytic solution for higher-dimensional quasi-spherical collapse with a specific equation of state, exploring the conditions for singularity formation and horizon development.

Findings

End state of collapse with $p=-\rho$ matches that of dust in one lower dimension.

Singularity formation depends on the equation of state and dimensionality.

Global collapse fate characterized by radial null geodesics.

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.