Classical solutions in the Einstein-Born-Infeld-Abelian-Higgs model

We consider the classical equations of the Born-Infeld-Abelian-Higgs model (with and without coupling to gravity) in an axially symmetric ansatz. A numerical analysis of the equations reveals that the (gravitating) Nielsen-Olesen vortices are smoothly deformed by the Born-Infeld interaction, characterized by a coupling constant ${\beta }^2,$ and that these solutions cease to exist at a critical value of ${\beta }^2.$ When the critical value is approached, the length of the magnetic field on the symmetry axis becomes infinite.