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    Paper   IPM / P / 12807
       School of Physics
      Title: Extremal Black Holes and First Law of Thermodynamics
      Author(s):
    1 . M. Johnstone
    2 . M.M. Sheikh-Jabbari
    3 . J. Simon
    4 . H. Yavartanoo
      Status: Published
      Journal: Phys. Rev. D
      Vol.: 88
      Year: 2013
      Pages: 101503
      Supported by: IPM
      Abstract:
    We study low temperature expansion of the first law of thermodynamics for near extremal black holes. We show that for extremal black holes with non-vanishing entropy, the leading order contribution yields an expression for their extremal entropy in agreement with the entropy function result and the Cardy formula for the entropy of a two dimensional chiral conformal field theory (CFT). When their entropy vanishes due to the vanishing of a one-cycle on the horizon, such leading contribution is always compatible with the first law satisfied by a BTZ black hole. These results are universal and consistent both with the presence of local AdS2 and AdS3 near horizon throats for extremal black holes and the suggested quantum microscopic descriptions (AdS2/CFT1, Kerr/CFT and EVH/CFT).

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