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Title: Mean Curvature Flow in Null Hypersurfaces and the Detection of MOTS
Abstract

We study the mean curvature flow in 3-dimensional null hypersurfaces. In a spacetime a hypersurface is called null, if its induced metric is degenerate. The speed of the mean curvature flow of spacelike surfaces in a null hypersurface is the projection of the codimension-two mean curvature vector onto the null hypersurface. We impose fairly mild conditions on the null hypersurface. Then for an outer un-trapped initial surface, a condition which resembles the mean-convexity of a surface in Euclidean space, we prove that the mean curvature flow exists for all times and converges smoothly to a marginally outer trapped surface (MOTS). As an application we obtain the existence of a global foliation of the past of an outermost MOTS, provided the null hypersurface admits an un-trapped foliation asymptotically.

 
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NSF-PAR ID:
10363349
Author(s) / Creator(s):
;
Publisher / Repository:
Springer Science + Business Media
Date Published:
Journal Name:
Communications in Mathematical Physics
Volume:
390
Issue:
3
ISSN:
0010-3616
Page Range / eLocation ID:
p. 1149-1173
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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