Introduction ; Preliminary tools ; Main theorem ; Comparison ; Error estimates ; Second fundamental form estimates for the components of ; Second fundamental form \mathbf {\chi }} estimating \mathbf {\chi }} and \mathbf {\zeta }} ; Uniformization theorem ; boldsymbol {\chi } on the surfaces boldsymbol {S} changes in boldsymbol {r} and boldsymbol {s} ; The last slice ; Curvature tensor-components ; Uniformation theorem: standard situation, cases 1 and 2 ; Introduction ; Norms and notation ; Existence theorem ; The electromagnetic field ; Error estimates for ; Interior estimates for ; Comparison theorem for the Weyl tensor ; Error estimates for ; Second fundamental form ; The lapse function ; Optical function ; Conclusion