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Generalizations of the Smarr formula for black holes with nonlinear electromagnetic fields
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We present a direct, geometric derivation of the generalized Smarr formula for the stationary axially symmetric black holes with nonlinear electromagnetic fields. The additional term is proven to be proportional to the integral of the trace of the electromagnetic energy-momentum tensor and can be written as a product of two conjugate variables. From the novel relation we can deduce all previously proposed forms of the generalized Smarr formula, which were derived only for the spherically symmetric black holes, and provide the lowest order quantum correction to the classical relation from the Euler-Heisenberg Lagrangian.
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Cited by 2 Pith papers
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Derivation of the Smarr formula from the Komar charge in Einstein-nonlinear electrodynamics theories and applications to regular black holes
Derives Smarr formula from generalized Komar charge in 4D Einstein-NLED theories by treating coupling constant as dynamical field, and analyzes thermodynamics of regular Bardeen black hole.
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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.
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