Speaker
Gustav Nilsson, Max-Plank-Institut für Gravitationsphysik (Albert-Einstein-Institut)
Abstract
For gravitational instantons of Petrov type D, we study Ricci-flat perturbations of the metric. Through a Riemannian analog of the Newman–Penrose formalism, we see that the linearized vacuum Einstein equations give rise to equations for the various components of the linearized Weyl curvature. In particular, we see that the equations for the components $\dot{\Psi}_0$ and $\dot{\tilde{\Psi}}_0$ decouple, giving rise to a Riemannian version of the Teukolsky equation. In the particular cases of the Riemannian Kerr and Taub-bolt instantons, the study of this equation leads to mode stability, which can be seen as a step toward rigidity.