The volume of marginally trapped submanifolds in a Lorentzian manifold satisfying the null energy condition

Abstract

In this paper, we focus on a marginally trapped submanifold f: Σⁿ → M₁ⁿ⁺² in a Lorentzian manifold M₁ⁿ⁺². We show that f lies in a certain null hypersurface in M₁ⁿ⁺² and f has a locally volume-maximizing property in if M₁ⁿ⁺² satisfies the null energy condition.