Mode Stability for Gravitational Instantons of Type D
Gustav Nilsson
TL;DR
This paper proves mode stability for Ricci-flat perturbations of type D gravitational instantons, showing no solutions exist that violate regularity and flatness conditions, advancing understanding of their rigidity.
Contribution
It establishes mode stability for type D gravitational instantons, a key step towards proving their rigidity and uniqueness.
Findings
Mode stability proven for Ricci-flat perturbations.
Teukolsky equation admits no regular, asymptotically flat solutions.
Supports rigidity conjectures for type D instantons.
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.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Cosmology and Gravitation Theories · Advanced Mathematical Physics Problems