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.

中文翻译：

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GRW时空中r陷阱子流形的刚性和不存在性结果

在本文中，我们介绍了浸泡在广义Robertson-Walker时空中的r陷阱子流形的概念，作为Penrose引入的陷阱子流形的一般化。考虑抛物线性和随机完整性等某些属性，我们证明了在某些GRW时空配置中r陷阱的刚性和不存在结果，最后，我们提供了r陷阱子流形的示例，其中一些也同时被陷阱，但是我们提供了实例证明r陷阱子流形的概念相应地与数r有所不同。