Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 21 (2025), 022, 13 pages      arXiv:2410.21210      https://doi.org/10.3842/SIGMA.2025.022

Mode Stability of Hermitian Instantons

Lars Andersson a, Bernardo Araneda b and Mattias Dahl c
a) Beijing Institute of Mathematical Sciences and Applications, Beijing 101408, P.R. China
b) School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, EH9 3FD, UK
c) Institutionen för Matematik, Kungliga Tekniska Högskolan, 100 44 Stockholm, Sweden

Received December 13, 2024, in final form March 24, 2025; Published online April 01, 2025

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.

Key words: gravitational instantons; stability; spinor methods.

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