A Rosen-type bi-metric universe and its physical properties

The paper studies a spacetime endowed with two stationary metrics. The first one is a Riemannian one, called the R-Schwarzschild metric. It satisfies Einstein vacuum field equations, describes correctly the slowdown of clocks in the gravitational field, the orbits of the planets and the perihelion drift. The R-Schwarzschild metric can be seen as the basic texture of the spacetime. All objects having mass are ruled by this Riemannian metric. The second metric, the light-adapted one, is deduced both taking into account the Rosen-type bi-metric compatibility condition and by the preservation of the axiom of the speed of the light limit. This second metric offers the texture of the “light-like” objects. The main “normal” surprise is that this metric can be only the classical Schwarzschild metric. So, a Rosen-type bi-metric universe exists and its properties are in accordance with the experimental physical evidences.