Extremal and weakly trapped submanifolds in generalized Robertson-Walker spacetimes

Pelegrín, José A. S.

doi:10.1016/j.jmaa.2021.125533

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2023

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(1 citation statement)

References 39 publications

(54 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our results in Section 6 generalize some previous results in the existing literature. Specifically, when applied to standard static spacetimes, we extend Proposition 2 in [24] and Theorem 4 in [26], and in the case of Generalized Robertson-Walker spacetimes we get in particular Results 5.1 and 5.2 in [8] and most of the rigidity and non-existence results in Section 4.1 in [27].…”

Section: Introductionmentioning

confidence: 63%

On complete trapped submanifolds in globally hyperbolic spacetimes

Albujer

Herrera

Rubio

2023

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

The aim of this manuscript is to obtain rigidity and non-existence results for complete (non necessarily compact) spacelike submanifolds with causal mean curvature vector ﬁeld in orthogonally splitted spacetimes. We also obtain results regarding the geometry of such submanifolds by ensuring, under some mild hypothesis, the non-existence of local minima or maxima of certain distinguished function.As an application in General Relativity, we obtain several nice results regarding (nonnecessarily closed) trapped surfaces in a huge family of spacetimes. In fact, we show how our technique allows us to recover in particular some relevant previous results for trapped surfaces in both, standard static spacetimes and Generalized Robertson-Walker spacetimes.

show abstract