Kaluza-Klein Monopole in AdS Spacetime

TL;DR

This paper constructs Kaluza-Klein monopole solutions in higher-dimensional Anti-de Sitter spacetimes, revealing that static monopoles require at least two extra dimensions, unlike in flat space.

Contribution

It demonstrates the non-existence of five-dimensional static KK monopoles in AdS and establishes the dimensional requirements for such solutions.

Findings

No five-dimensional static KK monopole in AdS

At least two extra dimensions needed for static KK monopoles in AdS

Static KK monopoles do not smoothly reduce to flat space solutions

Abstract

We construct analogs of the flat space Kaluza-Klein (KK) monopoles in locally Anti-de Sitter (AdS) spaces for $D \ge 5+1$. We show that, unlike the flat space KK monopole, there is no five dimensional static KK monopole in AdS that smoothly reduces to the flat space one as the cosmological constant goes to zero. Thus, one needs at least two extra dimensions, one of which is compact, to get a static KK monopole in cosmological backgrounds.