LAUSR

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 slow down 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. 1. Historical preliminaries The well known Einstein’s equations of the gravitational field with the cosmological modification are: Rij − 1 2 gijR− gijΛ = 8πG c4 Tij . They link the curvature of the spacetime to the matter it contains, which means that they describe how matter and energy determine the curvature of the spacetime. It is not very easy to determine these equations. In simple words, Einstein connected the divergence of the Ricci tensor via Bianchi’s identity to the conservation of the Energy-Momentum tensor. Technically speaking, Einstein succeeded to find a divergence free mixed tensor Rh k − 1 2δ h kR, which covariant form Rij− 12gijR differs to the energy-momentum tensor Tij by a multiplicative constant. Here R := Rh h = g Rsh is the scalar curvature. Then, since the Newtonian field equation ∇2φ = 4πGρ can be replaced by the new field equation ∇2φ− Λφ = 4πGρ, Einstein proposed the zero-divergence tensor Rij − 12gijR− gijΛ as a left member of the gravitational field equation. In the particular case when the gravitational field is produced by a single massive body that is concentrated in a small region of space, Einstein established the relativistic vacuum field equations: