2012/05/08 by Marc Mars
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Geometric Analysis and Curvature Flows #gr-qc
paper · pdf · doi:10.1088/0264-9381/29/14/145019
29 pages, no figures
arxiv created 2012/05/08 · openalex publication_date 2012/06/26 · arxiv updated 2015/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Closed sections of totally geodesic null hypersurfaces are marginally outer trapped surfaces (MOTS), for which a well-defined notion of stability exists. In this paper we obtain the explicit form for the stability operator for such MOTS and analyse in detail its properties in the particular case of non-evolving horizons, which include both isolated and Killing horizons. We link these stability properties with the surface gravity of the horizon and/or to the existence of minimal sections. The results are used, in particular, to obtain an area–angular momentum inequality for sections of axially symmetric horizons in four spacetime dimensions, which helps clarifying the relationship between two different approaches to this inequality existing in the literature.