Noncommutative geometry adds a Planck-scale parameter Θ to Schwarzschild-AdS black hole thermodynamics, producing van der Waals fluid behavior and phase transitions while preserving the first law.
Alavi, Reissner-Nordstrom black hole in noncommutative spaces, Acta Phys.Polon.B40:2679-2687,2009
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Non-commutative geometry and thermodynamics of the Schwarzschild-AdS black hole
Noncommutative geometry adds a Planck-scale parameter Θ to Schwarzschild-AdS black hole thermodynamics, producing van der Waals fluid behavior and phase transitions while preserving the first law.