Null hypersurfaces and trapping horizons. (arXiv:1706.03861v1 [math.DG])

The purpose in this work is to study (marginally) trapped submanifolds lying in a null hypersurface. Let $(M,g,N)\rightarrow \overline{M}(c)$ be a null hypersurface of a Lorentzian space form, 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 $M$ is totally umbilical then leaves of the screen distribution are space forms with known sectional curvature. In particular, in a spacetime $\overline{M}(c)$ with constant sectional curvature $c$, cross-sections of a Non-Expanding Horizon are space forms of the same sectional curvature. We also show that a null Monge hypersurface graph of a function $F$ is a trapping horizon if and only if $F$ is harmonic. 查看全文>>