  We prove a continuation condition in the context of 3+1 dimensional vacuum
Einstein gravity in Constant Mean extrinsic Curvature (CMC) gauge. More
precisely, we obtain quantitative criteria under which the physical spacetime
can be extended in the future indefinitely as a solution to the Cauchy problem
of the Einstein equations given regular initial data. In particular, we show
that a gauge-invariant $H^{2}$ Sobolev norm of the spacetime Riemann curvature
remains bounded in the future time direction provided the so-called deformation
tensor of the unit timelike vector field normal to the chosen CMC hypersurfaces
verifies a spacetime $L^\infty$ bound. To this end, we implement a novel
technique to obtain this refined estimate by using Friedlander's parametrix for
tensor wave equations on curved spacetime and Moncrief's subsequent
improvement. We conclude by providing a physical explanation of our result as
well as its relation to the issues of determinism and weak cosmic censorship.
