Electrostatic spherically symmetric configurations in gravitating nonlinear electrodynamics

TL;DR

This paper analyzes gravitating electrostatic spherically symmetric solutions in nonlinear electrodynamics coupled to gravity, revealing how their structure depends on flat space solutions and identifying new features for finite-energy solitons.

Contribution

It characterizes the structure of G-ESS solutions in admissible nonlinear electrodynamics models, linking them to flat space behaviors and exploring new qualitative features for finite-energy solitons.

Findings

G-ESS solutions are determined by flat space asymptotics.

Divergent-energy solutions resemble Reissner-Nordström structure.

Finite-energy solutions exhibit new qualitative features related to mass, charge, and energy.

Abstract

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-Nordstr\"om 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.