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Coupling Constants as Conserved Charges in Black Hole Thermodynamics

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arxiv 2309.07634 v2 pith:DJ5CSWGG submitted 2023-09-14 gr-qc hep-th

Coupling Constants as Conserved Charges in Black Hole Thermodynamics

classification gr-qc hep-th
keywords theoryblackcouplingschargesconservedconstantscouplingfields
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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In a generic theory of gravity coupled to matter fields, the Smarr formula for black holes does not work properly if the contributions of the coupling constants defining the theory are not incorporated. However, these couplings, such as the cosmological constant or the dimensionful parameters that appear in the Lagrangian, are fixed parameters defining the theory, and they cannot be varied. Here, we present a robust method, applicable to any covariant Lagrangian, that upgrades the role of the couplings from being constants in the theory to being free parameters of the solutions. To this end, for each one of the couplings in a theory, a pair of auxiliary scalar and gauge fields is introduced. The couplings are shown to be conserved charges of the global part of the implemented gauge symmetry. Besides, their conjugate chemical potentials are defined as the electric potential of the corresponding gauge fields on the black hole horizon. Using this method, we systematically extend the first law and the Smarr formula by coupling conserved charges and their conjugate potentials. The thermodynamics of a black hole solution in a quadratic gravity theory is given as an example.

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Cited by 5 Pith papers

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  3. An Exact Single-Rotating Near-Horizon Geometry in Einstein-Gauss-Bonnet Gravity

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    Presents the first analytic singly rotating near-horizon solution in 5D Einstein-Gauss-Bonnet gravity with finite curvature invariants for limited rotation.

  4. Gravitational constant as a conserved charge in black hole thermodynamics

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    Using two scalar-gauge pairs and the off-shell ADT formalism in a modified Einstein-Hilbert theory, the authors derive conserved charges for mass, cosmological constant, and G that yield a consistent extended thermody...

  5. Extended symmetry of the Maxwell theory with a gauge coupling constant as a conserved charge

    hep-th 2026-01 unverdicted novelty 5.0

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