Topological Charged Black Holes in High Dimensional Spacetimes and Their Formation from Gravitational Collapse of a Type II Fluid

Abstract

Topological charged black holes coupled with a cosmological constant in $R^2\times X^{D-2}$ spacetimes are studied, where $X^{D-2}$ is an Einstein space of the form ${}^{(D-2)}{R}_{AB}=k(D-3)h_{AB}$. The global structure for the four-dimensional spacetimes with $k=0$ is investigated systematically. The most general solutions that represent a Type $II$ fluid in such a high dimensional spacetime are found, and showed that topological charged black holes can be formed from the gravitational collapse of such a fluid. When the spacetime is (asymptotically) self-similar, the collapse always forms black holes for $k=0,-1$, in contrast to the case $k=1$, where it can form either balck holes or naked singularities.

14 figures, to appear in Phys. Rev. D