Weak field approximation in a model of de Sitter gravity: Schwarzschild-de Sitter solutions

TL;DR

This paper explores weak field solutions in de Sitter gravity, revealing singularities at the center and identifying regular solutions that could explain galactic rotation curves without dark matter.

Contribution

It derives all regular solutions in a de Sitter gravity model under weak field approximation, potentially offering an alternative explanation for galactic rotation curves.

Findings

Solutions are singular at the center if exterior is Schwarzschild-de Sitter.

All regular solutions are identified and characterized.

Regular solutions may explain galactic rotation curves without dark matter.

Abstract

The weak field approximation in a model of de Sitter 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 de Sitter spacetime. It is shown on one hand that any solution should be singular at the center of the matter field, if the exterior is described by a Schwarzschild-de Sitter 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.