A Smarr formula for charged black holes in nonlinear electrodynamics

Abstract

It is well known that the Smarr formula does not hold for black holes in non-linear electrodynamics. The main reason for this is the fact that the trace of the energy momentum tensor for nonlinear electrodynamics does not vanish as it is for Maxwell's electrodynamics. Starting from the Komar integral, we derived a new Smarr-type formula for spherically symmetric static electrically charged black hole solutions in nonlinear electrodynamics. We show that this general formula is in agreement with some that are obtained for black hole solutions with nonlinear electrodynamics.

v2: 17 pages, 3 figures, added note, four added references

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• Thermodynamics and P-v criticality of Bardeen-AdS Black Hole in 4-D Einstein-Gauss-Bonnet Gravity
• Black Holes With Many Horizons in the Theories of Nonlinear Electrodynamics
• Quark-antiquark confinement and nonlinear electrodynamics
• Einstein-non-linear Maxwell-Yukawa black hole
• Novel charged black hole solutions of Born-Infeld type: General properties, Smarr formula and Quasinormal frequencies