Topology of cosmological black holes

Abstract

Motivated by the question of how generic inflation is, I study the time-evolution of topological surfaces in an inhomogeneous cosmology with positive cosmological constant Λ. If matter fields satisfy the Weak Energy Condition, non-spherical incompressible surfaces of least area are shown to expand at least exponentially, with rate d log Amin/dλ ⩾ 8π GNΛ, under the mean curvature flow parametrized by λ. With reasonable assumptions about the nature of singularities this restricts the topology of black holes: (a) no trapped surface or apparent horizon can be a non-spherical, incompressible surface, and (b) the interior of black holes cannot contain any such surface.