Regularity for Lorentz metrics under curvature bounds

@article{Anderson2002RegularityFL,
  title={Regularity for Lorentz metrics under curvature bounds},
  author={Michael T. Anderson},
  journal={Journal of Mathematical Physics},
  year={2002},
  volume={44},
  pages={2994-3012}
}
Let (M, g) be an (n+1)-dimensional space–time, with bounded curvature, with respect to a bounded framing. If (M, g) is vacuum, or satisfies a weak condition on the stress-energy tensor, then it is shown that (M, g) locally admits coordinate systems in which the Lorentz metric g is well-controlled in the (space–time) Sobolev space L2,p, for any p<∞. This result is essentially optimal. The result allows one to control the regularity of limits of sequences of space–times, with uniformly bounded… 
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