An explicit covariant formula for thermodynamic volume is derived that universally decomposes into explicit Lagrangian coupling dependence plus dynamical field response contributions.
Equiv- alence of Noether charge and Hilbert action boundary term formulas for the black hole entropy in F(Rabcd) gravity theory,
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Background subtraction for black hole thermodynamics is valid and equivalent to Iyer-Wald in matter-coupled gravity theories, with smooth performance in examples but subtleties for certain matter fields.
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Explicit and covariant formula for thermodynamic volume in extended black hole thermodynamics
An explicit covariant formula for thermodynamic volume is derived that universally decomposes into explicit Lagrangian coupling dependence plus dynamical field response contributions.
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Validity of the Background Subtraction Method for Black Hole Thermodynamics in Matter-Coupled Gravity Theories
Background subtraction for black hole thermodynamics is valid and equivalent to Iyer-Wald in matter-coupled gravity theories, with smooth performance in examples but subtleties for certain matter fields.