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Conformal Weyl gravity and perihelion precession
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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.
Forward citations
Cited by 2 Pith papers
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Atomic clocks and gravitational waves as probes of non-metricity
The paper claims existing gravitational-wave data already bound Weyl non-metricity, α²ω̄0<10⁻⁶⁹ GeV, via backreaction of a Planck-scale Weyl field, but a dropped kinetic term numerically exceeds the assumed sensitivity.
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Modified gravity from Weyl connection and the $f(R,\cal{A})$ extension
Weyl-connection gravity with a dynamical vector field produces an effective dark energy sector, recovering Lambda-CDM in one class and dynamical dark energy in others.
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