Cosmological-static metric correspondence and Kruskal type solutions from symmetry transformations

Abstract

We develop a formalism which provides a new view for the transformation of spherically symmetric metrics, regarding cosmological and Kruskal type metrics. Our analysis begins with some general relevant dynamical metrics in cosmology, and prove that they all can be transformed to a unique static form. We extend the formalism to obtain generalized Kruskal type coordinates in cosmology and black hole theory. This extended formalism provides a novel mechanism to obtain suitable coordinate charts associated with spherically symmetric metrics. In particular, we obtain explicitly new Kruskal type coordinates for extremal Reissner-Nordström and Schwarzschild-de-Sitter metrics, as well for an extension of the de-Sitter metric.