Liouville solution in General Relativity with a scalar field

Abstract

New one parameter family of exact solutions in General Relativity with a scalar field has been found. The metric is of Liouville type which admits complete separation of variables in the geodesic Hamilton–Jacobi equation. This solution exists for the exponential potential for a scalar field and is invariant with respect to global Lorentz transformations. It describes, in particular, a black hole formation and evolution of space-time with a naked singularity. Solutions corresponding to the naked singularity provide accelerating expansion of the homogeneous and isotropic Universe only inside the light cone, and can be smoothly continued through the zero of the scale factor along geodesics to infinite past.