Regularity for Lorentz metrics under curvature bounds

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 L-2,L-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 curvature, and has applications to the structure of boundaries and extensions of space-times. (C) 2003 American Institute of Physics.