2017/06/12 by Hans Fotsing T., T., Hans Fotsing, Ferdinand Ngakeu +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1706.03861
openalex publication_date 2017/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The purpose of the present work is to study (marginally) trapped submanifolds lying in a null hypersurface. Let (M,g,N)→\Bm(c) be a null hypersurface of a space-time with constant sectional curvature c, endowed with a Screen Integrable and Conformal rigging N. The (Marginally) Trapped Submanifolds we are interested with are particular leaves of the screen distribution according to the sign of their expansions. We prove that if c is non-positive, then \Bm cannot contain a null non-expanding horizon. In the case c is positive, we show that if \Bm satisfies Einstein's equation and dominant energy condition holds, then any null trapping horizon of \Bm is a null non-expanding horizon. More generally we prove that in a spacetime \Bm(c) with constant sectional curvature c, cross-sections of a marginally outer trapped tube are Riemann manifold with the same constant sectional curvature c.