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.

Kaluza–Klein-type models of de Sitter and Poincaré gauge theories of gravity

“…Since S T is invariant under the gauge transformation (22), δS T given by Eqs. (26) and (27) should be equal to zero. Therefore,…”

“…It is remarkable that the dS gravity model becomes highly non-trivial when the exterior (vacuum) solutions are required to join some interior solutions [24][25][26]. For example, the spin-current-free matter in torsionless interior solutions must be distributed uniformly [24] because equation (42) sets a new constraint.…”

“…For example, the spin-current-free matter in torsionless interior solutions must be distributed uniformly [24] because equation (42) sets a new constraint. In the torsional case, the exterior solutions can join with the interior solutions with the non-uniformly distributed matter field, satisfying Newton's law in the weak field approximation, and supply an alternative way to explain the galactic rotation curves without involving the dark matter [25,26]. But unfortunately, the model may be inconsistent with the solar-system-scale observations, since the Schwarzschild-dS solutions, which play an important role in the explanation of the solar-system-scale observations, could not be smoothly connected to regular internal solutions, in the weak field approximation [26].…”