Rigidity and Nonexistence Results for r -Trapped Submanifold in GRW Spacetimes

In this paper, we introduce the notion of r -trapped submanifolds immersed in generalized Robertson–Walker spacetimes as generalization of the trapped submanifolds introduced by Penrose. Considering some properties such as parabolicity and stochastic completeness, we prove rigidity and nonexistence results for r -trapped in some configurations of GRW spacetimes and, lastly, we provide examples of r -trapped submanifolds, some of them are also simultaneously trapped, but we provided examples proving that the notion of r -trapped submanifolds is different accordingly to the number r .