  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.
