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: | 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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