Electrically charged black holes supported by non-linear electrodynamics

Abstract: In this talk we discuss several aspects of black holes with electric charge within General Relativity. We first consider the historical context and different applications of non-linear electrodynamics in the physics of black holes and Cosmology. Then we construct general non-linear electrodynamics as functions of the fundamental field invariants and classify them according to the nature of their electrostatic spherically symmetric solutions. Finally we consider the coupling to gravity of these models, and discuss the features of their associated black hole solutions in terms of horizons, singularities and thermodynamics, and we conclude the talk by discussing several extensions to other gravitational backgrounds.