The purpose of this paper is to establish from local hypothesis (i.e. from assumptions made on an arbitrary small region of spacetime in the vicinity of the black hole) some results concerning the final state topology of black holes. Main theorem. Let \(V\) be a standard static body in spacetime surrounding \(k \geq 0\) black holes; hence, in particular, \(\partial V= \partial^ H\cup \partial^ E\), where \(\partial^ H\) has \(k\) components, and \(\partial^ E\) is mean convex, orientable and has at least one 2-sphere component. Assume that the energy condition \((EC1)\), or, more generally, the energy condition \((EC2)\) is satisfied. Then \(\partial^ E\) is connected (and hence consists of a single 2-sphere), each component of \(\partial^ H\) is a 2-sphere, and \(V\) is diffeomorphic to a closed 3-ball minus \(k\) open 3-balls.