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In a theory where the cosmological constant $\Lambda$ or the gauge coupling constant $g$ arises as the vacuum expectation value, its variation should be included in the first law of thermodynamics for black holes.
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G.W. Gibbons, H. Lü, D.N. Page and C.N. Pope, The general Kerr-de Sitter metrics in all dimensions
2005
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G.W. Gibbons, M.J. Perry and C.N. Pope, Bulk/boundary thermodynamic equivalence, and the Bekenstein and cosmic-censorship bounds for rotating charged AdS black holes
2005
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Z.W. Chong, M. Cvetič, H. Lü and C.N. Pope, Charged rotating black holes in four-dimensional gauged and ungauged supergravities
2005
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Z.W. Chong, M. Cvetič, H. Lü and C.N. Pope, General non-extremal rotating black holes in minimal five-dimensional gauged supergravity
2005
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H. Liu, H. Lü, M. Luo and K.N. Shao, Thermodynamical metrics and black hole phase transitions
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B.P. Dolan, The cosmological constant and the black hole equation of state
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W. Ballik and K. Lake, The volume of stationary black holes and the meaning of the surface gravity
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D. Kastor, S. Ray and J. Traschen, Enthalpy and the mechanics of AdS black holes
2009
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2009
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