Mode Stability of Hermitian Instantons
General Relativity and Quantum Cosmology
2025-04-02 v3 Differential Geometry
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.
Keywords
Cite
@article{arxiv.2410.21210,
title = {Mode Stability of Hermitian Instantons},
author = {Lars Andersson and Bernardo Araneda and Mattias Dahl},
journal= {arXiv preprint arXiv:2410.21210},
year = {2025}
}