Tests of general relativity in pseudo-Newtonian approach

TL;DR

This paper evaluates how well pseudo-Newtonian potentials can replicate key tests of general relativity, highlighting their usefulness for insight and their limitations in modeling complex gravitational phenomena.

Contribution

It provides analytical expressions and assesses the accuracy of pseudo-Newtonian approaches for relativistic effects, clarifying their scope and limitations.

Findings

Pseudo-Newtonian potentials can reproduce Mercury's perihelion precession and gravitational redshift.

They fail to accurately model gravitational lensing across various impact parameters.

No single pseudo-Newtonian potential captures all relativistic effects universally.

Abstract

We investigate the extent to which pseudo-Newtonian gravitational potentials can reproduce classic tests of general relativity without resorting to full general relativistic formalisms. This is useful for the researchers seeking intuitive insight into relativistic gravity. Focusing on the perihelion precession of Mercury, gravitational redshift, and gravitational light bending, we derive analytical expressions for orbital precession and demonstrate that, with suitable physically acceptable parameters, pseudo-Newtonian approaches can accurately reproduce the observed perihelion advance and gravitational redshift. However, we confirm that no single potential consistently captures all relativistic effects. In particular, while certain parameters yield agreement with general relativity for planetary motion and redshift, they fail to reproduce gravitational lensing over a broad range of impact parameters. Our results highlight both the usefulness and limitations of pseudo-Newtonian methods in modeling gravitational phenomena. Although the pseudo-Newtonian approach cannot serve as universal substitutes for general relativity, especially in strong-field regimes, it provides valuable semi-analytical insight and pedagogical simplicity. Our results indicate the usefulness of the pseudo-Newtonian approach to uncover more complicated phenomena involved with strong field gravity in possibly modification to general relativity.