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 ${R}^{2}\ifmmode\times\else\texttimes\fi{}{X}^{D\ensuremath{-}2}$ spacetimes are studied, where ${X}^{D\ensuremath{-}2}$ is an Einstein space of the form ${}^{(D\ensuremath{-}2)}{R}_{\mathrm{AB}}=k(D\ensuremath{-}{3)h}_{\mathrm{AB}}.$ 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 show 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 $k=0,$ $\ensuremath{-}1,$ in contrast with the case $k=1,$ where it can form either black holes or naked singularities.