Mode Stability for Gravitational Instantons of Type D

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.

References in corpus (7)

• Mode stability on the real axis
• Gravitational instantons admit hyper-Kähler structure
• On toric Hermitian ALF gravitational instantons
• Topology of Toric Gravitational Instantons
• Gravitational Instantons and special geometry
• Gravitational instantons with $S^1$ symmetry
• Gravitational Instantons, Weyl Curvature, and Conformally Kaehler Geometry

Cited by in corpus (1)

• Topology of Toric Gravitational Instantons