Gravitational Collapse of Perfect Fluid in N-Dimensional Spherically Symmetric Spacetimes

Abstract

The Riemann, Ricci and Einstein tensors for N-dimensional spherically symmetric spacetimes in various systems of coordinates are studied, and the general metric for conformally flat spacetimes is given. As an application, all the Friedmann-Robertson-Walker-like solutions for a perfect fluid with an equation of state $p=k\rho$ are found. Then, these solutions are used to model the gravitational collapse of a compact ball, by first cutting them along a timelike hypersurface and then joining them with asymptotically flat Vaidya solutions. 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 symmetry, the formation of black holes always starts with a finite non-zero mass.

arXiv commentSome typos are corrected, and new references are added

References in corpus (3)

• Critical phenomena in gravitational collapse - Living Reviews
• Choptuik scaling in six dimensions
• The (Unstable) Threshold of Black Hole Formation

Cited by in corpus (4)

• Dimensional Dependence of Black Hole Formation in Self-Similar Collapse of Scalar Field
• Topological Charged Black Holes in High Dimensional Spacetimes and Their Formation from Gravitational Collapse of a Type II Fluid
• Developments in Black Hole Research: Classical, Semi-classical, and Quantum
• The role of the equation of state and the space-time dimension in spherical collapse