English

Local and global scalar curvature rigidity of Einstein manifolds

Differential Geometry 2022-12-21 v2

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.

Keywords

Cite

@article{arxiv.2109.09556,
  title  = {Local and global scalar curvature rigidity of Einstein manifolds},
  author = {Mattias Dahl and Klaus Kroencke},
  journal= {arXiv preprint arXiv:2109.09556},
  year   = {2022}
}

Comments

44 pages, final version, to appear in Math. Ann