First law and Smarr formula of black hole mechanics in nonlinear gauge theories

Yuan, Zhengqiu; Gao, Sijie

doi:10.1088/1361-6382/aac9d4

Cited by 41 publications

(31 citation statements)

References 39 publications

(61 reference statements)

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“…The Smarr formula is obtained from the total mass represented by the Komar integral, which can be separated into two parts [14]. The first part is a surface integral over the horizon, and gives κA/(4π); while the second one, including a deviation of the first law, is a volume integral with one boundary at spatial infinity and the other at event horizon [4,15], i.e.…”

Section: A Dymnikova Black Holementioning

confidence: 99%

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Gliner Vacuum, Self-consistent Theory of Ruppeiner Geometry for Regular Black Holes

Lan,

Miao

2021

Preprint

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By applying the idea of Gliner vacuum, we remove the anomalies in the first law of mechanics for regular black holes by introducing a natural V -PH term. The improved first law of mechanics redisplays the resemblance of black holes to traditional thermodynamic systems, which implies a restored correspondence of the mechanical variables to the thermodynamical ones. In particular, the linear relation A ∼ SBH remains unchanged. Based on this reconstruction, we establish a self-consistent theory of Ruppeiner geometry, and obtain a universal attractive property of microstructure for regular black holes.

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Section: A Dymnikova Black Holementioning

confidence: 99%

“…Regular black hole (RBH) is a system, of which the 1LM is deformed [4], such that the direct similarity of 1LM to thermodynamical law no longer holds. From this point, the RBHs do not have their corresponding 1LT, which is different from the traditional thermodynamical systems, and their Ruppeiner geometry is suspect.…”

Section: Introductionmentioning

confidence: 99%

Gliner Vacuum, Self-consistent Theory of Ruppeiner Geometry for Regular Black Holes

Lan,

Miao

2021

Preprint

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“…(12) is identically 0, which would be absurd since M is the black hole mass. The Smarr relation can nevertheless to be generalized to accommodate black holes coupled with nonlinear electromagnetic fields [12][13][14][15].…”

Section: Euler's Theorem For Quasi-homogeneous Functionsmentioning

confidence: 99%

A note on Smarr relation and coupling constants

Kuang

Ong

2019

Gen Relativ Gravit

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The Smarr relation plays an important role in black hole thermodynamics. It is often claimed that the Smarr relation can be written down simply by observing the scaling behavior of the various thermodynamical quantities. We point out that this is not necessarily so in the presence of dimensionful coupling constants, and discuss the issues involving the identification of thermodynamical variables. I. SMARR RELATION AND THE FIRST LAWThe fact that black holes behave like a thermodynamical system has dramatically changed our understanding of black holes ever since its conception in 1973 [1]. For an asymptotically flat Kerr-Newman black hole, the first law of black hole mechanics takes the formwhere M denotes the ADM mass of the black hole, S its Bekenstein-Hawking entropy, T its Hawking temperature, Q its electrical charge and J its angular momentum. The first law thus relates the various differential quantities. In some applications, one would like to work directly with the black hole parameters instead of their differentials. Fortunately, there is the Smarr relation [2]:where Φ denotes the electrical potential, while Ω denotes the angular velocity of the black hole. Smarr relations such as this have been widely studied in the literature, beyond the Kerr-Newman family. A good rule of thumb for writing down the Smarr relation for a given black hole is to look at the scaling (i.e. the dimensions) of the various thermodynamical quantities. See, e.g., Sec.2 of [3]. For example, in 4-dimensions, and in the units = k B = c = 1, we have M, Q ∝ L, and J, S ∝ L 2 , where L is a length scale. Due to Euler's theorem of quasi-homogeneous function (see below), we can simply write down M = M (S, Q, J) asFrom the first law (and the chain rule), one could identify the various partial derivatives and arrive at the Smarr relation, Eq.(2). Similarly, in the extended black hole

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“…Generalized Smarr formula for asymptotically flat and asymptotically AdS black holes A first generalization of the Smarr formula to elementary BH solutions of any G-NED in D = 4 was carried out in Ref. [70] (see also [93][94][95][96][97]). There, the deviation of the generalized formula in the general NED cases from the simple Smarr formula of the Reissner-Nordström case was identified in terms of the binding energies associated to the self-interactions of the electric field (due to the nonlinearities of the general NEDs), which contrasts with the linear character of Maxwell electrodynamics.…”

Section: Thermodynamic Relations and Scale Lawsmentioning

confidence: 99%

Structure and thermodynamics of charged nonrotating black holes in higher dimensions

2019

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We analyze the structural and thermodynamic properties of D-dimensional (D ≥ 4), asymptotically flat or Anti-de-Sitter, electrically charged black hole solutions, resulting from the minimal coupling of general nonlinear electrodynamics to General Relativity. This analysis deals with static spherically symmetric (elementary) configurations with spherical horizons. Our methods are based on the study of the behaviour (in vacuum and on the boundary of their domain of definition) of the Lagrangian density functions characterizing the nonlinear electrodynamic models in flat spacetime. These functions are constrained by some admissibility conditions endorsing the physical consistency of the corresponding theories, which are classified in several families, some of them supporting elementary solutions in flat space which are non topological solitons. This classification induces a similar one for the elementary black hole solutions of the associated gravitating nonlinear electrodynamics, whose geometrical structures are thoroughly explored. A consistent thermodynamic analysis can be developed for the subclass of families whose associated black hole solutions behave asymptotically as the Schwarzschild metric (in absence of a cosmological term). In these cases we obtain the behaviour of the main thermodynamic functions, as well as important finite relations among them. In particular, we find the general equation determining the set of extreme black holes for every model, and a general Smarr formula, valid for the set of elementary black hole solutions of such models. We also consider the one-parameter group of scale transformations, which are symmetries of the field equations of any nonlinear electrodynamics in flat spacetime. These symmetries are respected by the minimal coupling to gravitation and induce representations of the group in the spaces of solutions of the different models, characterized by their thermodynamic functions. Exploiting this fact we find the expression of the equation of state of the set of black hole solutions associated to any model. These results are generalized to asymptotically Anti-de-Sitter solutions.

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First law and Smarr formula of black hole mechanics in nonlinear gauge theories

Cited by 41 publications

References 39 publications

Gliner Vacuum, Self-consistent Theory of Ruppeiner Geometry for Regular Black Holes

Gliner Vacuum, Self-consistent Theory of Ruppeiner Geometry for Regular Black Holes

A note on Smarr relation and coupling constants

Structure and thermodynamics of charged nonrotating black holes in higher dimensions

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