# Limit of Universality of Entropy-Area Law for Multi-Horizon Spacetimes

- Published: 05 Sep 2011

- Daido University Japan

Then, because the thermal equilibrium system for BEH is the region Db, rb < r < rw, in Lorentzian SdS spacetime, we find the topology of Euclidean space of thermal equilibrium system for BEH is D2 × S2.

3 M − rb + 2 rw fw − √fw 5.4.1 where βb is the imaginary time period (5.27) and fw is in Eq.(5.30). Under the length size scaling (5.18), this temperature is scaled as Tb → λ−1 Tb. Therefore, by the assumption SdS-2, Tb is an intensive state variable of BEH.

2πrc2fw3/2 2rw 5.5.3 [5] S.W.Hawking, Particle Creation by Black Holes, Commun.Math.Phys.43 (1975) 199.

[20] S.Shankaranarayanan, Temperature Phys.Rev.D67 (2003) 084026.

[21] A.Strominger, The dS/CFT Correspondence, JHEP0110 (2001) 034. J.Kluson, Remark About dS/CFT Correspondence, Class.Quant.Grav.20 (2003) 2131. D.Astefanesei, R.B.Mann and E.Radu, Reisner-Nordstro¨m-de Sitter black hole, planar coordinates and dS/CFT, JHEP 0401 (2004) 029. A.Guijosa, D.A.Lowe and J.Murugan, A prototype for dS/CFT, Phys.Rev.D72 (2005) 046001.

[22] D.Kondepudi and I.Prigogine, Modern Thermodynamics, John Wiley & Sons, 1998. T.Tanaka, Methods of Statistical Mechanics, Cambridge Univ. Press, 2002. H.Tasaki, Thermodynamics (Netsu-Rikigaku), Baifu-Kan, 2000 (Published in Japanese). H.Tasaki, Statistical Mechanics (Tokei-Rikigaku), Baifu-Kan, 2008 (Published in Japanese).

[23] L.D.Landau and E.M.Lifshitz, Statistical Physics. Prat I, Pergamon, 1980.

[24] M.L.Bellac, Thermal Field Theory, Cambridge Univ. Press, 1996.