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Precession of perihelia in the Fisher metric

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 $σ$ 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.