Weak field approximation in a model of de Sitter gravity: Schwarzschild solutions and galactic rotation curves

Abstract

Weak field approximate solutions in the Λ → 0 limit of a model of de Sitter gravity have been presented in the static and spherically symmetric case. Although the model looks different from general relativity, among those solutions, there still exist the weak Schwarzschild fields with the smooth connection to regular internal solutions obeying the Newtonian gravitational law. The existence of such solutions would determine the value of the coupling constant, which is different from that of the previous literature. Moreover, there also exist solutions that could deduce the galactic rotation curves without invoking dark matter.

Weak Field Approximation in a Model of De Sitter Gravity: Schwarzschild–de Sitter Solutions

“…It shows that the Λ → 0 limit of the weak field approximation is not equivalent to the weak field approximation of the Λ → 0 limit discussed in Ref. [19]. In addition, all solutions of Eqs.…”

“…(7) be 1 : (−8πG), just like the case in GR. But it has been pointed [19] out that the Einstein term in our model plays a completely different role from that of GR. By Eq.…”

“…The result shows that the Λ → 0 limit of the weak field approximate equations is not equivalent to the weak field approximation of the Λ → 0 limit of the field equations, even when the Einstein-like equation is decomposed into its trace part, symmetric trace-free part and antisymmetric part, as discussed in Ref. [19].…”

“…In this paper, κ is to be determined. It has been pointed [19] out that when l → ∞, l 2 /κ should tend to a finite value. Therefore, 1/κ = O(1/l 2 ), and there does not exist first-order term in Eq.…”

“…In order to analyze the weak field approximation of the model, we have presented a way to tackle the above problem [19], in which the Λ → 0 limit is set after the Einstein-like equation is decomposed into its trace part, symmetric trace-free part and antisymmetric part. In this way, the weak field approximation for the static and spherically symmetric case has been studied [19]. It is found that there exist the solutions describing the weak Schwarzschild fields with nonzero torsion and the smooth connection to regular internal solutions obeying the Newtonian gravitational law.…”