Local and global scalar curvature rigidity of Einstein manifolds
arXiv:2109.09556 · doi:10.1007/s00208-022-02521-6
Abstract
An Einstein manifold is called scalar curvature rigid if there are no compactly supported volume-preserving deformation of the metric which increase the scalar curvature. We give various characterizations of scalar curvature rigidity for open Einstein manifolds as well as for closed Einstein manifolds. As an application, we construct mass-decreasing perturbations of the Riemannian Schwarzschild metric and the Taub-Bolt metric.
arXiv comment44 pages, final version, to appear in Math. Ann
References in corpus (9)
- Dynamic and Thermodynamic Stability and Negative Modes in Schwarzschild-Anti-de Sitter
- An Introduction to Conformal Ricci Flow
- Deformations of the hemisphere that increase scalar curvature
- Dynamical stability and instability of Ricci-flat metrics
- Stability of Einstein metrics under Ricci flow
- A mass for ALF manifolds
- Small eigenvalues of the Conformal Laplacian
- Stable and unstable Einstein warped products
- Semi-classical stability of AdS NUT instantons