Nonlinear perturbations of the Kaluza-Klein monopole

TL;DR

This paper investigates the nonlinear stability of the Kaluza-Klein monopole in five-dimensional vacuum Einstein equations, demonstrating asymptotic stability for small perturbations and collapse to black holes for large ones, with implications for M/String theory.

Contribution

It provides the first combined numerical and analytical evidence for the stability and instability regimes of the Kaluza-Klein monopole within a specific symmetry ansatz.

Findings

Kaluza-Klein monopole is asymptotically stable under small perturbations.

Large perturbations lead to collapse into a Kaluza-Klein black hole.

Results have implications for the stability of BPS states in M/String theory.

Abstract

We consider the nonlinear stability of the Kaluza-Klein monopole viewed as the static solution of the five dimensional vacuum Einstein equations. Using both numerical and analytical methods we give evidence that the Kaluza-Klein monopole is asymptotically stable within the cohomogeneity-two biaxial Bianchi IX ansatz recently introduced in \cite{bcs}. We also show that for sufficiently large perturbations the Kaluza-Klein monopole loses stability and collapses to a Kaluza-Klein black hole. The relevance of our results for the stability of BPS states in M/String theory is briefly discussed.