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.
Categories: gr-qc hep-th
