Precession of perihelia in the Fisher metric

TL;DR

This paper derives an expression for perihelion precession in the Fisher metric, incorporating both general relativistic effects and scalar field contributions, and constrains the scalar charge using Mercury's observational data.

Contribution

It provides a new formula for perihelion precession in the Fisher metric and establishes an observational upper bound on the scalar charge.

Findings

Derived perihelion precession expression including scalar field effects

Identified additional precession term due to scalar charge

Set an upper limit on scalar charge based on Mercury's precession data

Abstract

We study the precession of perihelia in the Fisher metric. Fisher metric is the solution of the Einstein's Equations with a massless scalar field as a coupling. We find an expression for the precession of perihelia in this metric. This expression contains general relativistic term for the precession of the perihelia and also an additional term which depends on the scalar field. Also, we obtain an upper bound on scalar charge $\sigma$ by using the observational value of the precession of perihelia for the Mercury planet and the discrepancy between this value and the general relativistic value.