Mode Stability for Gravitational Instantons of Type D
Differential Geometry
2024-05-22 v2 General Relativity and Quantum Cosmology
Abstract
We study Ricci-flat perturbations of gravitational instantons of Petrov type D. Analogously to the Lorentzian case, the Weyl curvature scalars of extreme spin-weight satisfy a Riemannian version of the separable Teukolsky equation. As a step towards rigidity of the type D Kerr and Taub-bolt families of instantons, we prove mode stability, i.e., that the Teukolsky equation admits no solutions compatible with regularity and asymptotic (local) flatness.
Keywords
Cite
@article{arxiv.2309.03972,
title = {Mode Stability for Gravitational Instantons of Type D},
author = {Gustav Nilsson},
journal= {arXiv preprint arXiv:2309.03972},
year = {2024}
}