Mode Stability of Hermitian Instantons

TL;DR

This paper proves the mode stability of certain Hermitian gravitational instantons, showing the positivity of the Teukolsky operator and discussing implications for stability and instabilities.

Contribution

It establishes the Riemannian analog of black hole mode stability for specific classes of Hermitian instantons, a novel extension in gravitational stability analysis.

Findings

Teukolsky operator is positive definite on these manifolds

Mode stability analogous to black hole stability is proven

Discussion of negative modes and variational instabilities

Abstract

In this note, we prove the Riemannian analog of black hole mode stability for Hermitian, non-self-dual gravitational instantons which are either asymptotically locally flat (ALF) and Ricci-flat, or compact and Einstein with positive cosmological constant. We show that the Teukolsky equation on any such manifold is a positive definite operator. We also discuss the compatibility of the results with the existence of negative modes associated to variational instabilities.