Nonlinear scattering of classical gravitons

The nonlinear classical graviton solution of the Einstein equations is given to second order in the null surface formulation (NSF). We solve the NSF field equations in a perturbative scheme that gives geometrical and finite results at each order of the expansion obtaining the main variables of the formalism to second order. Then, using an algebraic relationship with the NSF variables, we obtain the metric components and the nonlinear scattering of incoming gravitons. We also analyze the relevance of this result at a classical and quantum level.