Solitons of nonlinear scalar electrodynamics in general relativity

Solitons with spherical and/or cylindrical symmetry in the interacting system of scalar, electromagnetic, and gravitational fields have been obtained. As a particular case it is shown that the equations of motion admit a special kind of solution with a sharp boundary, known as droplets. For these solutions, the physical fields vanish and the space-time is flat outside of the critical sphere or cylinder. Therefore, the mass and the electric charge of these configurations are zero.