BOGOMOLNYI EQUATIONS IN THE EINSTEIN-YANG-MILLS-HIGGS SYSTEM

A static configuration of point charges held together by the gravitational attraction is known to be given by the Majumdar-Papapetrou solution in the Einstein-Maxwell theory. We consider a generalization of this solution to non-Abelian monopoles of the Yang-Mills-Higgs system coupled to gravity. The coupling to gravity is unconventional and the solution appears to have naked singularities. It is governed by an analogue of the Bogomol'nyi equations that bad played a central role in the analysis of non-Abelian monopoles.