Closed trapped surfaces in higher dimensional self-similar Vaidya solution

Abstract

Although an event horizon defines a black hole, it is difficult to explain a boundary of dynamical black holes. A trapped surface is a candidate of the boundary of dynamical black holes, and is studied in various spacetimes and settings. Usually, there is no trapped surface in a Minkowski region, however, Bengtsson and Senovilla showed an interesting result as follows: in a four-dimensional self-similar Vaidya spacetime, they considered non-spherical trapped surfaces and showed that trapped surfaces can extend into the Minkowski region, if and only if a mass function rises fast enough [1]. We extend this result in a higher-dimensional spacetime, because recently studying higher-dimensional black holes is significant in the context of large extra dimensions or TeV-scale gravity. In this paper we investigate a higher-dimensional Vaidya spacetime with a self-similar mass function. We match two kinds of (n + 1)-surfaces and construct trapped surfaces extended into the Minkowski region by using Bengtsson and Senovilla's way. Moreover, we demonstrate that there is no naked singularity, if the spacetime has trapped surfaces as above. These results might become a foothold to define the boundary of dynamical black holes in higher-dimensional spacetimes.