Let = ∪ Σt be a part of vacuum globally hyperbolic space-time (M, g), foliated by constant mean curvature hypersurfaces Σt with t0 < t* < 0. We improve the existing breakdown criteria for Einstein vacuum equations by showing that the foliation can be extended beyond t* provided the second fundamental form k and the lapse function n satisfy the weaker condition
The proof of this result %in particular relies on the second main result of the paper, which gives a uniform lower bound on the null radius of injectivity. © 2011 Wiley Periodicals, Inc.
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