Type II Fluid Solutions to Einstein Field Equations in N-Dimensional Spherical Spacetimes

TL;DR

This paper finds a broad class of Type II fluid solutions to Einstein's equations in N-dimensional spherical spacetimes, analyzing conditions for black hole or naked singularity formation during collapse.

Contribution

It introduces a generalized family of collapsing Vaidya solutions with self-similarity, revealing how the outcome depends on a dimension-dependent parameter.

Findings

Collapse leads to black holes when λ > λ_c(N).

Collapse results in naked singularities when λ < λ_c(N).

The critical parameter λ_c(N) depends only on the spacetime dimension N.

Abstract

A large class of Type II fluid solutions to Einstein field equations in N-dimensional spherical spacetimes is found, wich includes most of the known solutions. A family of the generalized collapsing Vaidya solutions with homothetic self-similarity, parametrized by a constant $\lambda$, is studied, and found that when $\lambda$ $>$ $\lambda_c(N)$, the collapse always forms black holes, and when $\lambda$ $<$ $\lambda_c(N)$, it always forms naked singularities, where $\lambda_c(N)$ is function of the spacetime dimension N only.