Don N. Page investigated equilibrium black-hole thermodynamics with Stephen Hawking. Their 1983 work showed that sufficiently large black holes in Anti-de Sitter spacetime can have positive heat capacity and coexist in stable thermal equilibrium with radiation.[ref]
Thermodynamics of black holes in anti-de Sitter space by Stephen Hawking and Don N. Page. Abstract and sections 2–3: temperature branches and canonical ensemble
The canonical ensemble distinguishes local stability from global preference: a locally stable black-hole solution need not have lower free energy than the competing thermal state.
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