Local existence in retarded time under a weak decay on complete null cones

In the previous paper (see Li and Zhu (2014)), for a characteristic problem with not necessarily small initial data given on a complete null cone decaying like that in the work of the stability of Minkowski spacetime by Christodoulou and Klainerman (1993), we proved the local existence in retarded t...

Full description

Saved in:
Bibliographic Details
Published in:Science China. Mathematics 2016, Vol.59 (1), p.85-106
Main Authors: Li, JunBin, Zhu, Xi-Ping
Format: Article
Language:English
Subjects:
Applications of Mathematics
Censorship
Cones
Decay
Decay rate
Infinity
Mathematical analysis
Mathematics
Mathematics and Statistics
Optimization
Stability
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In the previous paper (see Li and Zhu (2014)), for a characteristic problem with not necessarily small initial data given on a complete null cone decaying like that in the work of the stability of Minkowski spacetime by Christodoulou and Klainerman (1993), we proved the local existence in retarded time, which means the solution to the vacuum Einstein equations exists in a uniform future neighborhood, while the global existence in retarded time is the weak cosmic censorship conjecture. In this paper, we prove that the local existence in retarded time still holds when the data is assumed to decay slower, like that in Bieri’s work (2007) on the extension to the stability of Minkowski spacetime. Such decay guarantees the existence of the limit of the Hawking mass on the initial null cone, when approaching to infinity, in an optimal way.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-015-5056-7