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Entropy 2012, 14(11), 2291-2301; doi:10.3390/e14112291

Violation of the Third Law of Black Hole Thermodynamics inHigher Curvature Gravity

Department of General Education, Osaka Institute of Technology, 5-16-1, Omiya, Asahi-ku,Osaka, 535-8585, Japan
Received: 14 September 2012 / Revised: 31 October 2012 / Accepted: 8 November 2012 / Published: 12 November 2012
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We examine the weak version of the third law of black hole thermodynamics inthe n-dimensional Einstein–Gauss–Bonnet system with a negative cosmological constant.To see whether the extreme black hole solution with zero temperature is formed, weinvestigate the motion of the thin shell that has the equal mass to the extreme black holein the background described by the non-GR branch solutions. The interior of the shell isempty. Our analysis using the generalized Israel's junction condition shows that the shellcan contract beyond a certain radius and the degenerate horizon is formed for same range ofparameters. Hence, this model can be a counterexample of the third law.
Keywords: black holes; thermodynamics; modified gravity black holes; thermodynamics; modified gravity
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Torii, T. Violation of the Third Law of Black Hole Thermodynamics inHigher Curvature Gravity. Entropy 2012, 14, 2291-2301.

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