Vortices in the Bogomolnyi limit of Einstein-Maxwell-Higgs theory with or without external sources

The Abelian Higgs model with or without external particles is considered in curved space. Using the dual transformation, we rewrite the model in terms of dual gauge fields and derive the Bogomolnyi-type bound. We find all possible cylindrically symmetric vortex solutions and vortex-particle composites by examining the Einstein equations and the first-order Bogomolnyi equations. The underlying spatial manifold of these objects comprises a cylinder asymptotically and a two-sphere in addition to the well-known cone.