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

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• Euclidean and Hamiltonian thermodynamics for regular black holes
• Black Holes With Many Horizons in the Theories of Nonlinear Electrodynamics
• Quasinormal modes, greybody factors and thermodynamics of four dimensional AdS black holes in Critical Gravity
• Nonlinear electromagnetic fields in strictly stationary spacetimes
• Thermodynamics of Einstein-Euler-Heisenberg Black Holes with Thermal Fluctuations and Nonlinear Electromagnetic Fields
• Thermodynamics for regular black holes as intermediate thermodynamic states and quasinormal frequencies
• Quark-antiquark confinement and nonlinear electrodynamics
• Lagrangian reverse engineering for regular black holes
• Euclidean methods and phase transitions for the strongest deformations compatible with Schwarzschild asymptotics
• Quasilocal Smarr relations for static black holes
• Holographic Heat Engines Coupled with Logarithmic $U(1)$ Gauge Theory
• Schwarzschild spacetime immersed in test nonlinear electromagnetic fields
• Gravitational Lensing of Euler-Heisenberg Black Hole Surrounded by Perfect Fluid Dark Matter
• Thermodynamic phase transition of Anti-de Sitter Reissner-Nordström black holes with exotic Einstein-Maxwell gravities
• Exploring non-perturbative effects on quasi-topological black hole thermodynamics
• Thermodynamical and dynamical stability of Einstein-Maxwell and extremal Einstein-Born-Infeld thin shells in $(2+1)$ dimensions