Non-minimally coupled Einstein-Yang-Mills field equations and Wu-Yang monopoles in Bertotti-Robinson spacetimes

Abstract

Bertotti-Robinson spacetimes are topologically AdS(2) x 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.