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 $\Lambda$. If matter fields satisfy the Weak Energy Condition, non-spherical incompressible surfaces of least area are shown to expand at least exponentially, with rate $d\log A_{\min }/d\lambda \ge 8\pi G_N\Lambda$, 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.

JCAP version, 30 pages, 6 figures, our definition of black holes and apparent horizons in cosmology has been clarified

References in corpus (13)

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Cited by in corpus (1)

• On the initial singularity and extendibility of flat quasi-de Sitter spacetimes