REINTERPRETING GENERAL-RELATIVITY

We propose a 4-dimensional Kaluza-Klein formalism of general relativity of 4-dimensional space-times. This formalism is based on the (2,2)-splitting of 4-dimensional space-times, where the first two coordinates are interpreted as a-dimensional ''space-time'' coordinates and the second two as the 2-dimensional ''internal'' ones. Using the Kaluza-Klein variables, we present the 10 Einstein's equations in the Newman-Unti gauge. It turns out that the Einstein's theory can be interpreted as a 2-dimensional gauge theory of Yang-Mills type, whose gauge symmetry is the group of diffeomorphisms of the 2-dimensional ''internal'' space. We establish the equivalence of this Kaluza-Klein formalism and the null hypersurface formalism by expressing the Kaluza-Klein variables in terms of the null hypersurface variables.