# 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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