Topological censorship for Kaluza-Klein space-times

TL;DR

This paper extends topological censorship theorems to Kaluza-Klein space-times with weaker asymptotic conditions, proving simple connectedness and ruling out visible trapped surfaces, thus broadening the scope of topological constraints in higher-dimensional gravity.

Contribution

It introduces a version of topological censorship applicable to Kaluza-Klein asymptotics, enabling analysis of more general higher-dimensional space-times.

Findings

Proves simple connectedness of the quotient of the domain of outer communications.

Shows weakly trapped surfaces cannot be observed from infinity.

Extends topological censorship to broader asymptotic conditions.

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.