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

TL;DR

This paper demonstrates that in the Newtonian limit of Schwarzschild-de Sitter spacetime, light bending and Mercury's perihelion shift are consistent with full general relativity, clarifying the effects of the cosmological constant.

Contribution

It provides a simplified, Newtonian-based approach to understanding the influence of the cosmological constant on classical tests of general relativity.

Findings

Light bending results match full GR predictions up to a constant factor.

Mercury's perihelion shift aligns with full GR results.

The effects of the cosmological constant are clarified in a Newtonian framework.

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 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 $\Lambda$ in the general relativistic treatment of these phenomena.