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

Abstract

The perihelion precession and deflection of light have been investigated in the 4-dimensional general spherically symmetric spacetime, and the master equation is obtained. As the application of this master equation, the Reissner-Nordstorm-AdS solution and Clifton-Barrow solution in f (R) gravity have been taken as 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.