LETTER: Cosmological Constant, Conical Defect and Classical Tests of General Relativity

Abstract

We investigate the perihelion shift of the planetary motion and the bending of starlight in the Schwarzschild field modified by the presence of a Λ-term plus a conical defect. This analysis generalizes an earlier result obtained by Islam (Phys. Lett. A 97, 239, 1983) to the case of a pure cosmological constant. By using the experimental data we obtain that the parameter ǫ characterizing the conical defect is less than 10 −9 and 10 −7 , respectively, on the length scales associated with such phenomena. In particular, if the defect is generated by a cosmic string, these values correspond to limits on the linear mass densities of 10 19 g/cm and 10 21 g/cm, respectively.

Contribution of the cosmological constant to the relativistic bending of light revisited

“…The argument for the non-influence of Λ was apparently first made in [9] and has been re-made and reaffirmed by other authors, see for example [10,11,12,13,14]. The common basis of their arguments is that, in the Schwarzschild-de Sitter metric (first derived by Kottler [15]), which applies when Λ is included, Λ nevertheless drops out of the exact r, φ differential equation for a light path (null geodesic).…”

“…(17) in [9] and Eq. (22) in [10]. The orbit that is usually discussed is a small perturbation of the undeflected straight line in flat space r sin(φ) = R…”

Light deflection, lensing, and time delays from gravitational potentials and Fermat’s principle in the presence of a cosmological constant

“…The result made a correction to the question (see e.g. [5,6,7,8,9]) and was confirmed in [10,11,12]. Next, in reference [4], the authors brought the result into an observational context and used an exact solution construction where a Schwarzschild-de Sitter vacuole was embedded into a Friedmann-Lemaitre-Robertson-Walker (FLRW) background, and where a Λ-term was added to the deflection angle within the broadly used lens equation.…”

Hamilton-Jacobi approach for power-law potentials

“…therein). Indeed, one of the most elegant methods for describing geodesics and orbits of test particles in Schwarzchild and Kerr spacetimes, as well as for any stationary gravitational configuration, is provided by the relativistic HJ equation [3][4][5].…”