Black holes from generalized gauge field theories

Abstract: We summarize the main results of a broad analysis on electrostatic, spherically symmetric (ESS) solutions of a class of non-linear electrodynamics models minimally coupled to gravitation. Such models are defined as arbitrary functions of the two quadratic field invariants, constrained by several physical admissibility requirements, and split into different families according to the behaviour of these lagrangian density functions in vacuum and on the boundary of their domains of definition. Depending on these behaviours the flat-space energy of the ESS field can be finite or divergent. For each model we qualitatively study the structure of its associated gravitational configurations, which can be asymptotically \emph{Schwarzschild-like} or with an anomalous \emph{non Schwarzschild-like} behaviour at $r \rightarrow \infty$ (but being asymptotically flat and well behaved anyhow). The extension of these results to the non-abelian case is also briefly considered.