摘要A general calculation formula of the heat capacity for the HRN black holes is derived. The heat capacities for Q, Φ+ and r- fixed are obtained. Assuming that the charge-mass ratio of fluctuation modes does not exceed the extremal value, the minimum charge-mass ratio of the black holes for which the heat capacity is positive is determined.
Abstract：A general calculation formula of the heat capacity for the HRN black holes is derived. The heat capacities for Q, Φ+ and r- fixed are obtained. Assuming that the charge-mass ratio of fluctuation modes does not exceed the extremal value, the minimum charge-mass ratio of the black holes for which the heat capacity is positive is determined.
[1] Hawking S W 1972 Commun Math. Phys. 25 152 [2] Hawking S W 1975 Commun Math. Phys. 43 199 [3] Bardeen J M, Carter B and Hawking S W 1973 Commun.Math. Phys. 31 161 [4] Smarr L 1973 Phys. Rev. Lett. 30 71 [5] Jacobson T 1995 Phys. Rev. Lett. 75 1260 [6] Eling C, Guedens R and Jacobson T 2006 Phys. Rev.Lett. 96 121301 [7] Hayward S A 2004 Phys. Rev. Lett. 93 251101 [8] Ashtekar A and Krishnan B 2002 Phys. Rev. Lett. 89 261101 [9] Gong Y and Wang A 2007 Phys. Rev. Lett. 99211301 [10] Rogatko M 2007 Phys. Rev. D 75 124015 [11] Padmanabhan T 2005 Phys. Rept. 406 49 [12] Padmanabhan T 2002 Class. Quan. Grav. 19 5387 [13] Padmanabhan T 2004 Class. Quant. Grav. 214485 [14] Akbar M and Cai R G 2007 Phys. Lett. B 648243 [15] Cai R G and Cao L M 2007 Phys. Rev. D 75064008 [16] Sheykhi A, Wang B and Cai R G 2007 Phys. Rev. D 76 023515 [17] He T M and Zhang J Y 2007 Chin. Phys. Lett. 24 3336 [18] Jiang K X, Ke S M, Peng D T and Feng J 2009 Chin.Phys. Lett. 26 070401 [19] Weinhold F 1975 J. Chem. Phys. 63 2479 [20] Ruppeiner G 1979 Phys. Rev. A 20 1608 [21] Ruppeiner G 1995 Rev. Mod. Phys. 67 605 [22] Mrugala R 1984 Physica A 125 631 Salamon P, Nulton J D and Ihrig E 1984 J. Chem. Phys. 80 436 [23] Davies P C W 1977 Proc. Roy. Soc. Lond. A 353499 Davies P C W 1989 Class. Quant. Grav. 6 1909 [24] {\AAman J E, Bengtsson I and Pidokrajt N 2003 Gen.Rel. Grav. 35 1733 [25] Quevedo H 2007 J. Math. Phys. 48 013506 [26] Shen J, Cai R G, Wang B, Su R K 2005 Int. J. Mod.Phys. A 22 11 [27] Wei Y H 2008 Chin. Phys. Lett. 25 2782 [28] Gibbons G W, Horowitz G T and Townsend P K 1995 Class. Quantum Grav. 12 297 [29] Cai R G 1998 J. Korean Phys. Soc. 33 S477 [30] Quevedo H and S\'{anchez A 2008 J. High EnergyPhys. 0805 034
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