ABSTRACT
By searching a spacetime metric such that every particle follows a geodesic, Einstein had to consider a nonzero curvature Riemannian space. The previous equations play a fundamental role in the relativistic theory of Gravitation. Indeed, let us recall the Einstein equations in this theory are based on the fact that the gravitational potentials generalize the notions of Laplace and Poisson equations and establish relations between tensors in a Riemannian spacetime M4 • In the relativistic theory of Gravitation, the curvature of this manifold M 4 gives an account of gravitational phenomena. The coefficients gy of the metric (called gravitational potentials) are supposed to verify the Einstein equations describing the state ofenergetic distribution:
Ork=) Rrk-tgrkR=zrrk (8-70)
where Z is a constant linked to the gravitational constant and r is the stress-energy tensor.
