Conformal Weyl gravity and perihelion precession

TL;DR

This paper analyzes the perihelion precession in conformal Weyl gravity, revealing additional effects from a linear metric term and constraining its parameter using planetary data, extending previous galactic studies.

Contribution

It provides a detailed calculation of perihelion shift in conformal Weyl gravity and constrains the model parameter using solar system observations, linking it to galactic rotation results.

Findings

Perihelion shift includes a negative contribution from the linear term in the metric.

Constraints on the parameter gamma are consistent with galactic rotation curve data.

The linear term affects planetary motion predictions in conformal Weyl gravity.

Abstract

We investigate the perihelion shift of planetary motion in conformal Weyl gravity using the metric of the static, spherically symmetric solution discovered by Mannheim \& Kazanas (1989). To this end we employ a procedure similar to that used by Weinberg for the Schwarzschild solution, which has also been used recently to study the solar system effects of the cosmological constant $\Lambda$. We show that besides the general relativistic terms obtained earlier from the Schwarzschild - de Sitter solution, the expression for the perihelion shift includes a negative contribution which arises from the linear term $\gamma r$ in the metric. Using data for perihelion shift observations we obtain constraints on the value of the constant $\gamma$ similar to that obtained earlier using galactic rotational curves.