Electrostatic spherically symmetric configurations in gravitating nonlinear electrodynamics

We perform a study of the gravitating electrostatic spherically symmetric (G-ESS) solutions of Einstein field equations minimally coupled to generalized nonlinear Abelian gauge models in three space dimensions. These models are defined by Lagrangian densities which are general functions of the gauge field invariants, restricted by some physical conditions of admissibility. They include the class of nonlinear electrodynamics supporting electrostatic spherically symmetric (ESS) nontopological soliton solutions in absence of gravity. We establish that the qualitative structure of the G-ESS solutions of admissible models is fully characterized by the asymptotic and central-field behaviors of their ESS solutions in flat space (or, equivalently, by the behavior of the Lagrangian densities in vacuum and on the point of the boundary of their domain of definition, where the second gauge invariant vanishes). The structure of these G-ESS configurations for admissible models supporting divergent-energy ESS solutions in flat space is qualitatively the same as in the Reissner-Nordstrom case. In contrast, the G-ESS configurations of the models supporting finite-energy ESS solutions in flat space exhibit new qualitative features, which are discussed in terms of the Arnowitt-Deser-Misner mass, the charge, and the soliton energy. Most of the results concerning well-known models, such as the electrodynamics of Maxwell, Born-Infeld, and the Euler-Heisenberg effective Lagrangian of QED, minimally coupled to gravitation, are shown to be corollaries of general statements of this analysis.