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

TL;DR

This paper explores non-minimally coupled Einstein-Yang-Mills equations in Bertotti-Robinson spacetimes, revealing static solutions with Wu-Yang monopoles that could be relevant for quantum field vacuum polarization studies.

Contribution

It introduces a new class of static solutions combining Bertotti-Robinson metrics with Wu-Yang monopoles in a non-minimal coupling framework.

Findings

Static solutions with Wu-Yang monopoles identified

Potential relevance for quantum vacuum polarization effects

Extension of Einstein-Maxwell solutions to Einstein-Yang-Mills context

Abstract

Bertotti-Robinson spacetimes are topologically $AdS_2 \times S^2$ 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.