WEAK FIELD APPROXIMATION IN A MODEL OF DE SITTER GRAVITY: SCHWARZSCHILD–DE SITTER SOLUTIONS

Abstract

The weak field approximation in a model of de Sitter (dS) gravity is investigated in the static and spherically symmetric case, under the assumption that the vacuum spacetime without perturbations from matter fields is a torsion-free dS spacetime. It is shown on one the hand that any solution should be singular at the center of the matter field, if the exterior is described by a Schwarzschild–de Sitter (S–dS) spacetime and is smoothly connected to the interior. On the other, all the regular solutions are obtained, which might be used to explain the galactic rotation curves without involving dark matter.