J. Diaz-Alonso, D. Rubiera-Garcia
We perform a general study of the thermodynamic properties of static electrically charged black hole solutions of nonlinear electrodynamics minimally coupled to gravitation in three space dimensions. The Lagrangian densities governing the dynamics of these models in flat space are defined as arbitrary functions of the gauge field invariants, constrained by some requirements for physical admissibility. The exhaustive classification of these theories in flat space, in terms of the behaviour of the Lagrangian densities in vacuum and on the boundary of their domain of definition leads to the complete characterization of the associated families of gravitating electrostatic spherically symmetric solutions. We show how these results allow the determination of the thermodynamic properties of the corresponding black hole solutions. In this way, the thermodynamic laws are extended to the full class of asymptotically Schwarzschild-like black hole states, associated to the nine families of physically admissible models supporting this kind of solutions. Next, the generic behaviours of the relevant state variables for the sets of black hole solutions associated to the different families are classified and thoroughly analyzed in terms of the aforementioned boundary properties of the Lagrangians. Moreover, we establish universal scaling laws (holding for any admissible form of the Lagrangian densities) running several thermodynamic variables with the electric charge and the horizon radius. These laws form a one-parameter multiplicative group and lead to universal "renormalization group"-like first-order differential equations, whose beams of characteristics generate the full set of black hole states associated to any gravitating nonlinear electrodynamics. Some particular well known (and also other new) models are analyzed as illustrative examples of these procedures.
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http://arxiv.org/abs/1204.2506
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