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arXiv · 2606.30707

Dynamical Completion of Coupling-Charge Thermodynamics

Kamal Hajian·Bayram Tekin
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Abstract

The scalar-gauge pair formulation promotes gravitational coupling constants to conserved charges, clarifying their role in extended black hole thermodynamics. However, its original incarnation restricts these auxiliary scalar fields to rigid, non-dynamical configurations. In this paper, we introduce a local, dynamical completion of this framework. By constructing the kinetic sector from a defect, which is the difference between the top-form field strength and the associated gravitational Lagrangian density, we allow the scalar to propagate as a genuine massive degree of freedom. Crucially, this local sector acts as a charge-preserving massive scalar backreaction, ensuring the thermodynamic coupling remains a conserved integration constant rather than a locally varying field. When evaluated on constant-coupling configurations, the auxiliary stress-energy contributions vanish entirely, perfectly preserving the original black hole solutions, the first law, and the Smarr relation. We illustrate this construction using the cosmological constant and the Gauss-Bonnet coupling.

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Kamal Hajian, Bayram Tekin. 2026-06-29. Dynamical Completion of Coupling-Charge Thermodynamics. https://arxiv.org/abs/2606.30707

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