Cohomological uniqueness of the Cauchy problem solutions for the Einstein equation

In this paper we analyze the Cauchy problem for the Einstein equation in the case of a non-characteristic initial hypersurface. To find the correct notions for the characteristic and Cauchy data we introduce a complex, which we call the Einstein complex. Then the Cauchy problem acquires correctness in terms of the associated spectral sequence. We define the Cauchy data in such way that they allow us to reconstruct a cohomologously unique formal solution.