Abelian model of gravitating magnetic monopole (Q1060724)

A self-consistent U(1)-gauge model in gravitational field is investigated. The exact solutions of two types of corresponding field equations are obtained. These solutions can be interpreted as magnetic monopoles. The first solution is regular for \(r\neq 0\) and provides an everywhere regular geometry, the second one has a physical singularity. In order to guarantee the stability of the monopoles we introduce the notion of a gravitational topological charge using de Rham cohomology theory. This topological charge describes the sizes and the inner structure of the monopole.