Strong coupling expansion for general relativity

TL;DR

This paper develops a strong coupling expansion for vacuum Einstein equations in the ADM formalism, demonstrating its consistency with exact solutions and revealing that near singularities, spacetime dynamics are space homogeneous.

Contribution

It introduces a novel strong coupling expansion method for Einstein's equations in the ADM formalism, validated through a two-dimensional gravity model.

Findings

Expansion aligns with exact solutions in the Liouville model

Near singularities, spacetime dynamics become space homogeneous

Method provides insights into gravitational behavior close to singularities

Abstract

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.