Gravitational Collapse in Higher Dimensional Husain Space-Time

TL;DR

This paper analyzes gravitational collapse in higher-dimensional Husain space-time with various equations of state, revealing that the singularity's nature is mostly unaffected by these choices, except for the variable Chaplygin model.

Contribution

It provides exact solutions for gravitational collapse in higher dimensions with different fluid equations of state, and examines the resulting singularity characteristics.

Findings

Singularity nature is generally independent of the equation of state.

Variable Chaplygin model shows different singularity behavior.

Matching of Szekeres and Husain models is achieved.

Abstract

We investigate exact solution in higher dimensional Husain model for a null fluid source with pressure $p$ and density $\rho$ are related by the following relations (i) $p=k\rho$, (ii) $p=k\rho-\frac{B(v)}{\rho^{\alpha}}$ (variable modified Chaplygin) and (iii) $p=k\rho^{\alpha}$ (polytropic). We have studied the nature of singularity in gravitational collapse for the above equations of state and also for different choices of the of the parameters $k$ and $B$ namely, (i) $k=0$, $B=$ constant (generalized Chaplygin), (ii) $B=$ constant (modified Chaplygin). It is found that the nature of singularity is independent of these choices of different equation of state except for variable Chaplygin model. Choices of various parameters are shown in tabular form. Finally, matching of Szekeres model with exterior Husain space-time is done.