Foliations by spheres with constant expansion for isolated systems without asymptotic symmetry
Abstract
Motivated by the foliation by stable spheres with constant mean curvature constructed by Huisken-Yau, Metzger proved that every initial data set can be foliated by spheres with constant expansion (CE) if the manifold is asymptotically equal to the standard [t=0]-timeslice of the Schwarzschild solution. In this paper, we generalize his result to asymptotically flat initial data sets and weaken additional smallness assumptions made by Metzger. Furthermore, we prove that the CE-surfaces are in a well-defined sense (asymptotically) independent of time if the linear momentum vanishes.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2015
- DOI:
- 10.48550/arXiv.1501.02197
- arXiv:
- arXiv:1501.02197
- Bibcode:
- 2015arXiv150102197N
- Keywords:
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- Mathematics - Analysis of PDEs;
- General Relativity and Quantum Cosmology;
- Mathematics - Differential Geometry
- E-Print:
- 27 pages