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Let (M, g) be an (n+1) dimensional space-time, with bounded curvature withrespect to a bounded framing. If (M, g) is vacuum or satisfies a mild conditionon the stress-energy tensor, then we show that (M, g) locally admits coordinatesystems in which the Lorentz metric is well-controlled in the (space-time)Sobolev space L^{2,p}, for any finite p.Comment: 18p

Regularity for Lorentz metrics under curvature bounds