Area theorem and smoothness of compact Cauchy horizons

Abstract

We obtain an improved version of the area theorem for not necessarily differentiable horizons which, in conjunction with a recent result on the completeness of generators, allows us to prove that under the null energy condition every compactly generated Cauchy horizon is smooth and compact. We explore the consequences of this result for time machines, topology change, black holes and cosmic censorship. For instance, it is shown that compact Cauchy horizons cannot form in a non-empty spacetime which satisfies the stable dominant energy condition wherever there is some source content.

44 pages. v2: added Sect. 2.4 on the propagation of singularities and a second version of the area theorem (Theor. 14) which quantifies the area increase due to the jump set

References in corpus (5)

• The Raychaudhuri equations: a brief review
• Limit curve theorems in Lorentzian geometry
• Smoothness of compact horizons
• Completeness of Cauchy horizon generators
• The vacuum conservation theorem

Cited by in corpus (11)

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• Smoothness of compact horizons
• Wave equations with initial data on compact Cauchy horizons
• Surface gravity of compact non-degenerate horizons under the dominant energy condition
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• The annoying null boundaries
• What is a reduced boundary in general relativity?
• The boundary of the chronology violating set
• Optimal transport on null hypersurfaces and the null energy condition
• Horizon classification via Riemannian flows
• Regularity and temperature of stationary black hole event horizons