Causal Geometry of Einstein-Vacuum Spacetimes with Finite Curvature Flux
Analysis of PDEs
2016-09-07 v2 General Relativity and Quantum Cosmology
Mathematical Physics
Differential Geometry
math.MP
Abstract
One of the central difficulties of settling the -bounded curvature conjecture for the Einstein -Vacuum equations is to be able to control the causal structure of spacetimes with such limited regularity. In this paper we show how to circumvent this difficulty by showing that the geometry of null hypersurfaces of Enstein-Vacuum spacetimes can be controlled in terms of initial data and the total curvature flux through the hypersurface.
Keywords
Cite
@article{arxiv.math/0308123,
title = {Causal Geometry of Einstein-Vacuum Spacetimes with Finite Curvature Flux},
author = {Sergiu Klainerman and Igor Rodnianski},
journal= {arXiv preprint arXiv:math/0308123},
year = {2016}
}
Comments
The previous version has been corrected for minor errors and exposition