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

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 $λ$, is studied, and found that when $λ$ $>$ $λ_c(N)$, the collapse always forms black holes, and when $λ$ $<$ $λ_c(N)$, it always forms naked singularities, where $λ_c(N)$ is function of the spacetime dimension N only.