Smarr's formula for black holes with non-linear electrodynamics

Nora Breton

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Smarr's formula for black holes with non-linear electrodynamics

Nora Breton

General Relativity and Quantum Cosmology · Submitted 21 May 2004

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The same is done for the regular black hole solution derived by Ayon-Beato and Garcia, showing that in the case that variations of the electric charge are involved, the Smarr's formula does not longer is valid.

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It is known that for nonlinear electrodynamics the First Law of Black Hole Mechanics holds, however the Smarr's formula for the total mass does not. In this contribution we discuss the point and determine the corresponding expressions for the Bardeen black hole solution that represents a nonlinear magnetic monopole. The same is done for the regular black hole solution derived by Ayon-Beato and Garcia, showing that in the case that variations of the electric charge are involved, the Smarr's formula does not longer is valid.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	It is known that for nonlinear electrodynamics the First Law of Black Hole Mechanics holds, however the Smarr's formula for the total mass does not.	background 0.88	0.04	0.25	asserted 1.00
s1	In this contribution we discuss the point and determine the corresponding expressions for the Bardeen black hole solution that represents a nonlinear magnetic monopole.	contribution 1.00	0.85	0.10	asserted 0.91
s2	The same is done for the regular black hole solution derived by Ayon-Beato and Garcia, showing that in the case that variations of the electric charge are involved, the Smarr's formula does not longer is valid.	result 0.83	0.85	0.45	asserted 1.00

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Original abstract

It is known that for nonlinear electrodynamics the First Law of Black Hole Mechanics holds, however the Smarr's formula for the total mass does not. In this contribution we discuss the point and determine the corresponding expressions for the Bardeen black hole solution that represents a nonlinear magnetic monopole. The same is done for the regular black hole solution derived by Ayon-Beato and Garcia, showing that in the case that variations of the electric charge are involved, the Smarr's formula does not longer is valid.

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References

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Cited by 15 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Regular black holes do not violate the first law of thermodynamics
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For a D>=4 family of charged regular black holes sourced by nonlinear electrodynamics, the ordinary first law with Hawking temperature and area entropy holds on the fixed-theory solution space, and the reported correc...
Derivation of the Smarr formula from the Komar charge in Einstein-nonlinear electrodynamics theories and applications to regular black holes
gr-qc 2026-05 unverdicted novelty 7.0 of 10

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.
Rotating Black Holes in Einstein-Born-Infeld Theory
gr-qc 2025-07 conditional novelty 7.0 of 10

Exact rotating charged Einstein-Born-Infeld black holes are constructed numerically; they show charge-dependent extremal or naked-singularity endpoints, gyromagnetic ratio above 2, and ISCO radii below Kerr-Newman values.
Regular Black Holes in General Relativity from Nonlinear Electrodynamics with de Sitter Cores
gr-qc 2026-04 unverdicted novelty 6.0 of 10

Two new regular black-hole solutions with de Sitter cores, supported by magnetic nonlinear electrodynamics, are constrained by Sgr A* shadows and shown to be linearly stable under scalar perturbations.
P-V criticality in the extended phase space of Gauss-Bonnet black holes in AdS space
gr-qc 2013-06 accept novelty 6.0 of 10

In five-dimensional anti-de Sitter Gauss-Bonnet gravity the Gauss-Bonnet coupling alone produces van der Waals-like P-V criticality without electric charge, while in six and higher dimensions criticality requires the ...

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P-V criticality of charged AdS black holes
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A charged anti-de Sitter black hole, with the cosmological constant treated as pressure, reproduces the Van der Waals equation of state and its critical exponents (alpha=0, beta=1/2, gamma=1, delta=3).
Electrically charged regular black holes in higher dimensions: Maxwellian limit, branch point of the Lagrangian, and thermodynamics
gr-qc 2026-09 conditional novelty 5.0 of 10

A unified higher-dimensional regular Bardeen-Hayward black hole family is constructed, with matter recast as a fixed Hamiltonian theory that restores the standard first law and a branch point that can lie outside the ...
Two-scale magnetically charged regular black holes from nonlinear electrodynamics and a T-duality-inspired zero-point length
gr-qc 2026-08 conditional novelty 5.0 of 10

A two-parameter regular black hole family is constructed, with an explicit nonlinear electrodynamics source, exact thermodynamic identities, and analytic shadow and plasma-lensing predictions.
Field Sources for Dark Matter Black Holes
gr-qc 2026-05 unverdicted novelty 5.0 of 10

Dark matter halo profiles admit effective nonlinear electrodynamics completions that source regular black holes exhibiting de Sitter cores for finite central density and Schwarzschild asymptotics.
Nonlinear electrodynamics, regular black holes and wormholes
gr-qc 2017-10 conditional novelty 5.0 of 10

A new analytic dyonic solution in truncated Born-Infeld theory and a generalized class of time-dependent wormhole geometries are derived, with the wormhole-supporting Lagrangians shown to lack a Maxwell weak-field limit.
Gauss-Bonnet coupling constant as a free thermodynamical variable and the associated criticality
gr-qc 2013-11 conditional novelty 5.0 of 10

Treating 1/(8πα) as a thermodynamic pressure gives five-dimensional neutral Gauss-Bonnet AdS black holes a Van der Waals-like critical point with standard exponents, and gives charged higher-dimensional cases up to tw...
Extended phase space thermodynamics for charged and rotating black holes and Born-Infeld vacuum polarization
hep-th 2012-08 conditional novelty 5.0 of 10

Charged AdS black holes in any dimension d>3 reproduce Van der Waals criticality with mean-field exponents, while Born-Infeld black holes require a new quantity conjugate to the Born-Infeld parameter for the first law...
Black bounce sourced by non-minimally coupled linear electrodynamics and a canonical scalar field through a thin shell at the throat
gr-qc 2026-08 conditional novelty 4.0 of 10

A new family of black bounce and wormhole solutions in general relativity is constructed from a canonical scalar field non-minimally coupled to linear electrodynamics, with the required energy-condition violation conf...
Regular black holes sourced by nonlinear electrodynamics
gr-qc 2022-11 conditional novelty 4.0 of 10

Static, spherically symmetric regular black holes sourced by nonlinear electrodynamics require a magnetic charge, and new no-go theorems extend the electric and dyonic exclusions to Lagrangians depending on a fourth-o...
Critical behavior of charged Gauss-Bonnet AdS black holes in the grand canonical ensemble
hep-th 2014-04 accept novelty 4.0 of 10

The Van der Waals-like small-large black hole phase transition in the grand canonical extended phase space occurs only for five-dimensional spherical charged Gauss-Bonnet-AdS black holes with potential below the squar...

How the literature uses it

16 arXiv papers cite this in 17 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 11 sentences without a confident label

Cites it as background 6 papers

It has been known that the Born-Infeld parameter [ref] , the Gauss-Bonnet coupling constant [ref] , and the noncommutative parameter [ref] can be dealt with as a kind of thermodynamic pressure.

Thermodynamics of Horndeski black holes with non-minimal derivative coupling · Introduction · 0.87
Here we have analyses of the black hole thermodynamics for some specific theories (e.g. power-Maxwell in arbitrary number of dimensions [ref] , Born–Infeld [ref] , and Euler–Heisenberg [ref] ) or more general discussions (Smarr formula via assumed first law and scaling arguments [ref] ; electrically charged black holes [ref] but with highly implicit form of the first law and Smarr formula; Smarr formula for the $$-class NLE Lagrangian, using assumed first law and scaling argument [ref] ; various analyses of phase transitions in the presence of a cosmological constant and NLE fields [ref] ; thermodynamical stability [ref] ).

Black hole thermodynamics in the presence of nonlinear electromagnetic fields · Introduction · 0.98
NLED has been widely utilized in black hole physics, both as a mechanism for removing singularities [ref] and in studies of black hole thermodynamics [ref] .

Black hole solutions in Cotton gravity coupled to nonlinear electrodynamics · Introduction · 0.95

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