Generalizations of the Smarr formula for black holes with nonlinear electromagnetic fields

Abstract

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.

20 pages, v3: slightly revised, published version

References in corpus (13)

• Construction of Regular Black Holes in General Relativity
• Higher-dimensional black holes with a conformally invariant Maxwell source
• Higher-dimensional charged black holes solutions with a nonlinear electrodynamics source
• Conserved charges for black holes in Einstein-Gauss-Bonnet gravity coupled to nonlinear electrodynamics in AdS space
• Quantum Statistical Relation for black holes in nonlinear electrodynamics coupled to Einstein-Gauss-Bonnet AdS gravity
• Noncommutative $D_3$-brane, Black Holes and Attractor Mechanism
• Remarks on Heisenberg-Euler-type electrodynamics
• Killing Symmetries and Smarr Formula for Black Holes in Arbitrary Dimensions
• Probing nonlinear electrodynamics in slowly rotating spacetimes through neutrino astrophysics
• Conditions for nonexistence of static or stationary, Einstein-Maxwell, non-inheriting black-holes
• Nonlinear electromagnetic fields and symmetries
• On the various aspects of electromagnetic potentials in spacetimes with symmetries
• Observational constraints on electromagnetic Born-Infeld cosmology

Cited by in corpus (6)

• Thermodynamics and P-v criticality of Bardeen-AdS Black Hole in 4-D Einstein-Gauss-Bonnet Gravity
• Thermodynamics of the Euler-Heisenberg-AdS black hole
• Black Holes With Many Horizons in the Theories of Nonlinear Electrodynamics
• Quark-antiquark confinement and nonlinear electrodynamics
• Quasilocal Smarr relations for static black holes
• Schwarzschild spacetime immersed in test nonlinear electromagnetic fields