Topology of Cosmological Black Holes
  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 $\Lambda$. If matter fields satisfy the Weak
Energy Condition, non-spherical incompressible surfaces of least area are shown
to expand at least exponentially, with rate $d \log A_{\rm min}/d\lambda \geq
8\pi G_N\Lambda$, under the mean curvature flow parametrized by $\lambda$. 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.
