Black-Hole Thermodynamics from Gauge Freedom in Extended Iyer-Wald Formalism

Abstract

Thermodynamic systems admit multiple equivalent descriptions related by transformations that preserve their fundamental structure. This work focuses on exact isohomogeneous transformations (EITs), a class of mappings that keep fixed the set of independent variables of the thermodynamic potential, while preserving both the original homogeneity and the validity of a first law. Our investigation explores EITs within the extended Iyer--Wald formalism for theories containing free parameters (e.g., the cosmological constant). EITs provide a unifying framework for reconciling the diverse formulations of Kerr-anti de Sitter (KadS) thermodynamics found in the literature. While the Iyer--Wald formalism is a powerful tool for deriving first laws for black holes, it typically yields a non-integrable mass variation that prevents its identification as a proper thermodynamic potential. To address this issue, we investigate an extended Iyer--Wald formalism where mass and thermodynamic volume become gauge dependent. Within this framework, we identify the gauge choices and Killing vector normalizations that are compatible with EITs, ensuring consistent first laws. As a key application, we demonstrate how conventional KadS thermodynamics emerges as a special case of our generalized approach.

arXiv comment14 pages, published version

References in corpus (19)

• Black Hole Entropy is Noether Charge
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• Enthalpy and the Mechanics of AdS Black Holes
• Black hole chemistry: thermodynamics with Lambda
• Thermodynamics of Kerr-Newman-AdS Black Holes and Conformal Field Theories
• Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume
• Pressure and volume in the first law of black hole thermodynamics
• Rotation and the AdS/CFT correspondence
• The First Law of Thermodynamics for Kerr-Anti-de Sitter Black Holes
• Noether charge, black hole volume, and complexity
• Solution Phase Space and Conserved Charges: A General Formulation for Charges Associated with Exact Symmetries
• Contact Symmetries and Hamiltonian Thermodynamics
• The Vector Volume and Black Holes
• Extended black hole thermodynamics from extended Iyer-Wald formalism
• A Hamiltonian approach to Thermodynamics
• A Hamiltonian approach for the Thermodynamics of AdS black holes
• Extended quasilocal Thermodynamics of Schwarzchild-anti de Sitter black holes
• General mass formulas for charged Kerr-AdS black holes
• Generating Kerr-anti-de Sitter thermodynamics

Cited by in corpus (1)

• Hawking atmosphere of anti-de Sitter black holes