Classical tests of general relativity in the Newtonian limit of the Schwarzschild–de Sitter spacetime

Abstract

Recently it has been shown that despite previous claims the cosmological constant affects light bending. In the present article we study light bending and the advance of Mercury's perihelion in the context of the Newtonian limit of the Schwarzschild-de Sitter spacetime employing the special relativistic equivalence of mass and energy. In both cases, up to a constant factor, we find the same results as in the full general relativistic treatment of the same phenomena. These approximate and intuitive arguments demonstrate clearly what effects should have been expected from the presence of in the general relativistic treatment of these phenomena.

Effect of the Cosmological Constant on Light Deflection: Time Transfer Function Approach

“…We list in Table 1 the expressions of bending angle due to the cosmological constant previously obtained [14][15][16][17][18][19][20][21][22][23][24][25], and estimate the numerical value using c = 3.0 × 10 8 …”

“…Nevertheless, presently, it seems that a conclusion has not yet been reached, for instance, on whether the leading order effect due to Λ is coupled with the mass of the central body M or not. See [14] for a review and also [15][16][17][18][19][20][21][22][23][24][25]. In addition, for the cosmological constant and cosmological lensing equation, see, e.g., [17,18,26,27].…”

“…Also, as [13,14,[20][21][22]24,25], the cosmological constant leads to diminishing the bending angle due to the mass of the central body M.…”

Twist deformations of Newtonian Schwarzschild-(Anti-)de Sitter classical system

“…Recently, for example (see paper [2]) there has been studied the impact of such a force on the light bending. Besides the classical tests 2 of the Newtonian Schwarzschild-de Sitter space have been performed in article [3].…”

“…2 It has been studied the effects of cosmological constant Λ on Mercurys perihelion precession and light bending in the context of the Newtonian limit of SdS space-time. 3 In accordance with the Hopf-algebraic classification of all deformations of relativistic [25] and nonrelativistic [26] symmetries, one can distinguish three basic types of space-time noncommutativity (see also [27] for details): canonical [28]- [30], Lie-algebraic [30]- [33] and Quadratic deformation of Minkowski and Galilei spaces [30], [33]- [35]. 4 For details concerning the twist deformation of Hopf algebras see [36] and [37].…”