Hawking–Page Phase Transition

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In quantum gravity, the Hawking–Page phase transition is phase transition between AdS black holes with radiation and thermal AdS.^[1]

Stephen Hawking and Don Page ((Hawking Page)) showed that although AdS black holes can be in stable thermal equilibrium with radiation, they are not the preferred state below a certain critical temperature ${\displaystyle T_C}$. At this temperature, there will be a first order phase transition where below ${\displaystyle T_C}$, thermal AdS will become the dominant contribution to the partition function.

The Hawking-Page phase transition between the unstable small black hole to stable large black hole phase is understood as a confinement-deconfinement phase transition in the dual conformal field theory via AdS/CFT correspondence.^[2]

• Hawking, Stephen; Page, Don (1983), "Thermodynamics of black holes in anti-de Sitter space", Communications in Mathematical Physics 87 (4): 577–588, doi:10.1007/BF01208266, Bibcode: 1982CMaPh..87..577H, http://projecteuclid.org/euclid.cmp/1103922135 

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