Topological censorship for Kaluza-Klein space-times

Abstract

The standard topological censorship theorems require asymptotic hypotheses which are too restrictive for several situations of interest. In this paper we prove a version of topological censorship under significantly weaker conditions, compatible e.g. with solutions with Kaluza-Klein asymptotic behavior. In particular we prove simple connectedness of the quotient of the domain of outer communications by the group of symmetries for models which are asymptotically flat, or asymptotically anti-de Sitter, in a Kaluza-Klein sense. This allows one, e.g., to define the twist potentials needed for the reduction of the field equations in uniqueness theorems. Finally, the methods used to prove the above are used to show that weakly trapped compact surfaces cannot be seen from Scri.

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References in corpus (2)

• Global solutions of the Einstein-Maxwell equations in higher dimensions
• On higher dimensional black holes with abelian isometry group

Cited by in corpus (8)

• Covariant canonical formulations of classical field theories
• Globally hyperbolic spacetimes: slicings, boundaries and counterexamples
• States of a chiral 2d CFT
• Uniqueness theorems for Kaluza-Klein black holes in five-dimensional minimal supergravity
• A classification of supersymmetric Kaluza-Klein black holes with a single axial symmetry
• On the topology of initial data sets with higher genus ends
• Reflection Symmetry in Higher Dimensional Black Hole Spacetimes
• Topological censorship in spacetimes compatible with $\Lambda >0$