A new variation scheme using dS multipliers on horizon field equations yields the first law of black hole thermodynamics for general unconstrained changes in M, J, Q.
Thermodynamic Interpretation of the Field Equations of BTZ Charged Black Hole near the Horizon.Nuovo Cim
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A Constraint-Free Formulation of Black Hole Thermodynamics from the Field Equations
A new variation scheme using dS multipliers on horizon field equations yields the first law of black hole thermodynamics for general unconstrained changes in M, J, Q.