Five-dimensional perfect fluid collapse with the cosmological constant

This paper is devoted to the study of a five-dimensional spherically symmetric perfect fluid collapse with a positive cosmological constant. We take a five-dimensional spherically symmetric metric in the interior region and a five-dimensional Schwarzschild-de Sitter metric in the exterior region. The junction conditions between the interior and the exterior spacetimes are derived. By assuming that the energy density and the pressure satisfy the weak energy condition, we discuss the solution for the interior spacetime with a perfect fluid for both the marginally bound and the non-marginally bound cases. We investigate the apparent horizons and their physical significance and conclude that the cosmological constant slows down the collapse of matter and, hence, limits the size of the black hole. This analysis generalizes four-dimensional perfect fluid collapse. The energy density is found to diverge faster in five dimensions than in four dimensions, indicating faster collapse here. Also, the cosmological horizon and the black hole horizon have larger proper areas than they do in four dimensions.