Teleparallelism as a universal connection on null hypersurfaces in general relativity

We show that there exists a close relationship between inner geometry of a null hypersurfaceN ₃ and the Newman-Penrose (NP) spin coefficient formalism. Projecting the null complexNP tetrad ontoN ₃ we get two triads of basis vectors inN ₃. Inner geometry ofN ₃ is based on the assumption that these vectors are parallelly transported along the surface; this gives rise to the teleparallel connection as a metric nonsymmetric affine connection. The gauge freedom for the choice of the basis triads is given by the isotropy subgroup of the local Lorentz group leaving invariant the direction of the null generators ofN ₃, and teleparallelism is determined by the equivalence class of the basis triads with respect to the global gauge group. Nine of the twelve NP coefficients are identified as the triad components of the torsion and the second fundamental form ofN ₃. The resulting generalized Gauss-Codazzi equations are identical to 9 of the NP equations, i.e., to the half of the Ricci identities. This result gives a geometrical meaning to the entire formalism. Finally we present a general proof of Penrose's theorem that the shear of the null generators ofN ₃ is the only initial null datum for a gravitational field onN ₃.