Rigidity of free boundary MOTS. (July 2022)

• Record Type: Journal Article
• Authors: Mendes, Abraão
• Is Part Of: Nonlinear analysis. Volume 220(2022)
• Publication Date: 2022-07
• Subjects: Initial data sets -- Marginally outer trapped surfaces -- Free boundary surfaces -- Splitting results; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.112841
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The aim of this work is to present an initial data version of Hawking's theorem on the topology of black hole spacetimes in the context of manifolds with boundary. More precisely, we generalize the results of G.J. Galloway and R. Schoen (Galloway et al., 2006) and G.J. Galloway (Galloway, 2008; Galloway, 2018) by proving that a compact free boundary stable marginally outer trapped surface (MOTS) Σ in an initial data set with boundary satisfying natural dominant energy conditions (DEC) is of positive Yamabe type, i.e. Σ admits a metric of positive scalar curvature with minimal boundary, provided Σ is outermost. To do so, we prove that if Σ is a compact free boundary stable MOTS which does not admit a metric of positive scalar curvature with minimal boundary in an initial data set satisfying the interior and the boundary DEC, then an outer neighborhood of Σ can be foliated by free boundary MOTS Σ t, assuming that Σ is weakly outermost. Moreover, each Σ t has vanishing outward null second fundamental form, is Ricci flat with totally geodesic boundary, and the dominant energy conditions saturate on Σ t .