We perform a study of the gravitating electrostatic spherically symmetric (G-ESS) solutions of Einstein field equations minimally coupled to generalized non-linear 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 non-linear electrodynamics supporting ESS non-topological 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 behaviours of their ESS solutions in flat space (or, equivalently, by the behaviour 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-Nordström 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 ADM 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.

We perform a general analysis of the dynamic structure of two classes of relativistic lagrangian field theories exhibiting static spherically symmetric non-topological soliton solutions. The analysis is concerned with (multi-) scalar fields and generalized gauge fields of compact semi-simple Lie groups. The lagrangian densities governing the dynamics of the (multi-) scalar fields are assumed to be general functions of the kinetic terms, whereas the gaugeinvariant lagrangians are general functions of the field invariants. These functions are constrained by requirements of regularity, positivity of the energy and vanishing of the vacuum energy, defining what we call "admissible" models. In the scalar case we establish the general conditions which determine exhaustively the families of admissible lagrangian models supporting this kind of finite-energy solutions. We analyze some explicit examples of these different families, which are defined by the asymptotic and central behaviour of the fields of the corresponding particle-like solutions. From the variational analysis of the energy functional, we show that the admissibility constraints and the finiteness of the energy of the scalar solitons are necessary and sufficient conditions for their linear static stability against small charge-preserving perturbations. Furthermore we perform a general spectral analysis of the dynamic evolution of the small perturbations around the statically stable solitons, establishing their dynamic stability. Next, we consider the case of many-components scalar fields, showing that the resolution of the particle-like field problem in this case reduces to that of the one-component case. The study of these scalar models is a necessary step in the analysis of the gauge fields. In this latter case, we add the requirement of parity invariance to the admissibility constraints. We determine the general conditions defining the families of admissible gauge-invariant models exhibiting finiteenergy electrostatic spherically symmetric solutions which, unlike the (multi-) scalar case, are not always stable. The variational analysis of the energy functional leads now to supplementary restrictions to be imposed on the lagrangian densities in order to ensure the linear stability of the solitons. We establish a correspondence between any admissible soliton-supporting (multi-) scalar model and a family of admissible generalized gauge models supporting finite-energy electrostatic point-like solutions. Conversely, for each admissible soliton-supporting gauge-invariant model there is an associated unique admissible (multi-) scalar model with soliton solutions. This shows the exhaustive character of the admissibility and stability conditions in determining the class of soliton-supporting generalized gauge models. The usual Born-Infeld electrodynamic theory and its non-abelian extensions are shown to be (very particular) examples of one of these families.