Causality in nonlinear electrodynamics forces the entropy-to-mass-squared ratio of black holes to decrease with mass and the extremal mass-to-charge ratio to increase with charge.
Triple Points of Gravitational AdS Solitons and Black Holes
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abstract
We present a triple point of a new kind for General Relativity, at which two gravitational solitons can coexist with a planar black hole in anti de Sitter space. Working in the context of non-linear electrodynamics, we obtain simple, sensible spacetimes for which the thermodynamics can be studied in an analytic manner. The spacetimes are charged under the non-linear electrodynamics leading to an electric charge for black holes and a magnetic flux for solitons. In the grand-canonical ensemble, we show that the phase space of the theory is very rich, containing re-entrant phase transitions, as well as triple points, for small values of the coupling controlling the non-linearity of the electrodynamics Lagrangian.
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Causality Constraints on Black Hole Thermodynamics in Nonlinear Electrodynamics
Causality in nonlinear electrodynamics forces the entropy-to-mass-squared ratio of black holes to decrease with mass and the extremal mass-to-charge ratio to increase with charge.