Collapsing Perfect Fluid in Higher Dimensional Spherical Spacetimes

TL;DR

This paper derives solutions for perfect fluid collapse in higher-dimensional spherically symmetric spacetimes, revealing how self-similarity influences black hole formation and mass gaps.

Contribution

It provides the first comprehensive set of homogeneous and isotropic solutions for perfect fluids in N-dimensional conformally flat spacetimes, analyzing their role in gravitational collapse.

Findings

Black holes form with zero mass in self-similar collapse.

Collapse without self-similarity exhibits a mass gap at black hole formation.

Solutions extend previous 4D models to higher dimensions.

Abstract

The general metric for N-dimensional spherically symmetric and conformally flat spacetimes is given, and all the homogeneous and isotropic solutions for a perfect fluid with the equation of state $p = \alpha \rho$ are found. These solutions are then used to model the gravitational collapse of a compact ball. It is found that when the collapse has continuous self-similarity, the formation of black holes always starts with zero mass, and when the collapse has no such a symmetry, the formation of black holes always starts with a mass gap.