Non-Minimally Coupled Einstein-Yang-Mills Field Equations and Wu-Yang Monopoles in Bertotti-Robinson Spacetimes

Abstract

Bertotti-Robinson spacetimes are topologically $Ad{S}_2\times S^2$ and described by a conformally flat metric. Together with the Coulomb electric potential, they provide a class of static, geodetically complete Einstein-Maxwell solutions. We show here that the Bertotti-Robinson metric together with Wu-Yang magnetic pole potentials give a class of static solutions of a system of non-minimally coupled Einstein-Yang-Mills equations that may be relevant for investigating vacuum polarization effects in a first order perturbative approach to quantum fields.

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• The Refractive Index of Curved Spacetime: the Fate of Causality in QED
• Non-minimal Wu-Yang monopole
• Non-minimal $\ln (R)F^2$ Couplings of Electromagnetic Fields to Gravity: Static, Spherically Symmetric Solutions
• Electric Charge Screening By Non-Minimal Couplings Of Electromagnetic Fields To Gravity