Mean curvature flow in null hypersurfaces and the detection of MOTS

Roesch, Henri and Scheuer, Julian ORCID: https://orcid.org/0000-0003-2664-1896 2022. Mean curvature flow in null hypersurfaces and the detection of MOTS. Communications in Mathematical Physics 390 , pp. 1149-1173. 10.1007/s00220-022-04326-9

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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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Uncontrolled Keywords:	Mean curvature flow, Marginally outer trapped surfaces, General relativity, Null geometry
Publisher:	Springer
ISSN:	0010-3616
Funders:	National Science Foundation, DMS-1703184, Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), SCHE 1879/3-1
Date of First Compliant Deposit:	31 January 2022
Date of Acceptance:	12 January 2022
Last Modified:	12 May 2023 06:31
URI:	https://orca.cardiff.ac.uk/id/eprint/146735

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