Solutions to mean curvature equations in weighted standard static spacetimes

Abstract

In this article, we study the solutions for the mean curvature equation in a weighted standard static spacetime, ℙnƒ x ρℝ1, having a warping function ρ whose weight function ƒ does not depend on the parameter t ∈ ℝ. We establish a ƒ-parabolicity criterion to study the rigidity of spacelike hypersurfaces immersed in ℙnƒ x ρℝ1 and, in particular, of entire Killing graphs constructed over the Riemannian base ℙn. Also we give applications to weighted standard static spacetimes of the type Gn x ρℝ1, where Gn is the Gaussian space.