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.
Thermodynamics of spacetime: The einstein equation of state.Physical Review Letters, 75(7):1260–1263
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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.