Strong coupling expansion for general relativity

Strong coupling expansion is computed for the Einstein equations in vacuum in the Arnowitt-Deser-Misner (ADM) formalism. The series is given by the duality principle in perturbation theory as presented in [M.Frasca, Phys. Rev. A 58, 3439 (1998)]. An example of application is also given for a two-dimensional model of gravity expressed through the Liouville equation showing that the expansion is not trivial and consistent with the exact solution, in agreement with the general analysis. Application to the Einstein equations in vacuum in the ADM formalism shows that the spacetime near singularities is driven by space homogeneous equations.