A Note on the Instability of Lorentzian Taub-NUT-Space

TL;DR

This paper demonstrates that Lorentzian Taub-NUT space is linearly unstable under generic perturbations, which may explain difficulties in establishing a consistent thermodynamics for NUT-charged spacetimes.

Contribution

It proves the linear instability of Lorentzian Taub-NUT space against SU(2)-invariant perturbations, highlighting a fundamental challenge in understanding NUT-charged spacetime thermodynamics.

Findings

No SU(2)-invariant tensorial perturbations exist.

Lorentzian Taub-NUT space is linearly unstable.

Instability may hinder thermodynamic formulations.

Abstract

I show that there are no SU(2)-invariant (time-dependent) tensorial perturbations of Lorentzian Taub-NUT space. It follows that the spacetime is unstable at the linear level against generic perturbations. I speculate that this fact is responsible for so far unsuccessful attempts to define a sensible thermodynamics for NUT-charged spacetimes.