About the parabolicity of trapped submanifolds in standard static spacetimes

Abstract

In this work, we introduce the concept of totally trapped submanifolds immersed in a Lorentzian manifold. Moreover, we obtain some uniqueness or non-existence results for (p,ψ)-parabolic submanifolds immersed in standard static spacetimes (SSST). In particular, we derive some rigidity results for this type of submanifolds which guarantee that, under appropriate hypothesis, the only ones are those contained in slices. In order to obtain these results we study the height function associated to the submanifold using the (p,ψ)-Laplacian for ψ a function associated to the warping function of the SSST.