Variational and rigidity properties of static potentials
Variational and rigidity properties of static potentials
In this paper we study some global properties of static potentials on asymptotically flat $3$-manifolds $(M,g)$ in the nonvacuum setting. Heuristically, a static potential $f$ represents the (signed) length along $M$ of an irrotational timelike Killing vector field, which can degenerate on surfaces corresponding to the zero set of $f$. …