Discrete and finite general relativity

We develop the general theory of relativity in a formalism with extended ca usality that describes physical interaction through discrete, transversal a nd localized pointlike fields. The essence of this approach is of working w ith fields defined with support on straight lines and not on hypersurfaces as usual. The general relativity homogeneous held equations are then solved for a finite, singularity-free, point-like field that we associate with a 'classical graviton'. The standard Einstein continuous formalism is retriev ed by means of an averaging process, and its continuous solutions are deter mined by the chosen imposed symmetry. The Schwarzschild metric is obtained by imposing spherical symmetry on the averaged field.