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arXiv · 2309.03972

Mode Stability for Gravitational Instantons of Type D

Gustav Nilsson
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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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Gustav Nilsson. 2023-09-07. Mode Stability for Gravitational Instantons of Type D. https://doi.org/10.1088/1361-6382%2Fad296f

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