Nonlinear stability of the Taub-NUT soliton in 6+1 dimensions

TL;DR

This paper demonstrates the nonlinear stability of the 6+1 dimensional Taub-NUT soliton under small symmetric perturbations and explores its collapse into a black hole under stronger disturbances, including the black hole's existence and properties.

Contribution

It provides the first evidence of nonlinear stability for the 6+1 dimensional Taub-NUT soliton and characterizes the black hole formed from strong perturbations, including its mass.

Findings

Taub-NUT soliton is asymptotically nonlinearly stable under small perturbations.

Strong perturbations lead to collapse into a black hole.

Existence and properties of the black hole are established, including mass calculation.

Abstract

Using mixed numerical and analytical methods we give evidence that the 6+1 dimensional Taub-NUT soliton is asymptotically nonlinearly stable against small perturbations preserving biaxial Bianchi IX symmetry. We also show that for sufficiently strong perturbations the soliton collapses to a warped black hole. Since this black hole solution is not known in closed form, for completeness of the exposition we prove its existence and determine its properties. In particular, the mass of the black hole is computed.