Perihelion precession and deflection of light in the general spherically symmetric spacetime

TL;DR

This paper derives a main equation for perihelion precession and light deflection in general spherically symmetric spacetimes, applying it to specific solutions in $f(R)$ gravity and analyzing the effects of charge and cosmological constant.

Contribution

It introduces a unified main equation for these phenomena and clarifies the influence of charge and $f(R)$ gravity, addressing misconceptions about solar electric charge effects.

Findings

Electric charge and $f(R)$ gravity influence perihelion precession and light deflection.

Cosmological constant affects only perihelion precession.

Sun's electric charge cannot explain the discrepancy in Mercury's perihelion precession.

Abstract

In this paper, the perihelion precession and deflection of light have been investigated in the 4-dimensional general spherically symmetric spacetime, and the main equation is obtained. As the application of this main equation, the Reissner-Nordstorm-AdS solution and Clifton-Barrow solution in $f(R)$ gravity have been taken for the examples. We find that both the electric charge and $f(R)$ gravity can affect the perihelion precession and deflection of light, while the cosmological constant can only effect the perihelion precession. Moreover, we clarify a subtlety in the deflection of light in the solar system that the possible sun's electric charge is usually used to interpret the gap between the experiment data and theoretical result. However, after also considering the effect from the sun's same electric charge on the perihelion precession of Mercury, we can find that it is not the truth.