×

\(f(R)\) black holes as heat engines. (English) Zbl 1373.83074

Summary: With the cosmological constant considered as a thermodynamic variable in the extended phase space, it is natural to study the thermodynamic cycles of the black hole, which is conjectured to be performed using renormalization group flow. We first investigate the thermodynamic cycles of a 4-dimensional asymptotically AdS \(f(R)\) black hole. Then we study the thermodynamic cycles of higher dimensional asymptotically AdS \(f(R)\) black holes. It is found that when \(\Delta V \ll \Delta P\), the efficiency of isobar-isochore cycles running between high temperature \(T_H\) and low temperature \(T_C\) will increase to its maximum value, which is exactly the Carnot cycles’ efficiency both in 4-dimensional and in higher dimensional cases. We speculate that this property is universal for AdS black holes, if there is no phase transition in the thermodynamic cycle. This result may deepen our understanding of the thermodynamics of the AdS black holes.

MSC:

83C57 Black holes
80A10 Classical and relativistic thermodynamics
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
81T17 Renormalization group methods applied to problems in quantum field theory
83E15 Kaluza-Klein and other higher-dimensional theories
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Hawking, SW, No article title, Nature, 248, 30 (1974) · Zbl 1370.83053 · doi:10.1038/248030a0
[2] Bekenstein, JD, No article title, Phys. Rev. D, 9, 3292 (1974) · doi:10.1103/PhysRevD.9.3292
[3] Kubiznak, D.; Mann, RB, No article title, JHEP, 07, 033 (2012) · Zbl 1397.83072 · doi:10.1007/JHEP07(2012)033
[4] Gunasekaran, S.; Mann, RB; Kubiznak, D., No article title, JHEP, 11, 110 (2012) · doi:10.1007/JHEP11(2012)110
[5] Altamirano, N.; Kubiznak, D.; Mann, RB, No article title, Phys. Rev. D, 88, 101502 (2013) · doi:10.1103/PhysRevD.88.101502
[6] Cai, RG; Cao, LM; Li, L.; Yang, RQ, No article title, JHEP, 09, 005 (2013) · doi:10.1007/JHEP09(2013)005
[7] Mo, JX; Liu, WB, No article title, Eur. Phys. J, C74, 2836 (2014) · doi:10.1140/epjc/s10052-014-2836-0
[8] Zhang, LC; Ma, MS; Zhao, HH; Zhao, R., No article title, Eur. Phys. J., C74, 3052 (2014) · doi:10.1140/epjc/s10052-014-3052-7
[9] Mo, JX; Liu, WB, No article title, Phys. Rev. D., 89, 084057 (2014) · doi:10.1103/PhysRevD.89.084057
[10] Hendi, SH; Panahiyan, S.; Panah, BE; Momennia, M., No article title, Eur. Phys. J., C75, 507 (2015) · doi:10.1140/epjc/s10052-015-3701-5
[11] Lan, SQ; Mo, JX; Liu, WB, No article title, Eur. Phys. J., C75, 419 (2015) · doi:10.1140/epjc/s10052-015-3641-0
[12] Wei, SW; Liu, YX, No article title, Phys. Rev. Lett., 115, 111302 (2015) · doi:10.1103/PhysRevLett.115.111302
[13] Penrose, R., No article title, Riv. Nuovo Cim., 1, 252 (1969)
[14] Abbott, BP; etal., No article title, Phys. Rev. Lett., 116, 061102 (2016) · doi:10.1103/PhysRevLett.116.061102
[15] Johnson, CV, No article title, Class. Quant. Grav., 31, 205002 (2014) · Zbl 1304.83031 · doi:10.1088/0264-9381/31/20/205002
[16] Dolan, BP, No article title, Class. Quant. Grav., 28, 235017 (2011) · Zbl 1231.83020 · doi:10.1088/0264-9381/28/23/235017
[17] Wei, S.W., Liu, Y.X (2016)
[18] Sadeghi, J., Jafarzade, K.: arXiv:1504.07744[hep-th] (2015)
[19] Johnson, CV, No article title, Entropy, 18, 120 (2016) · doi:10.3390/e18040120
[20] Moon, T.; Myung, YS; Son, EJ, No article title, Gen. Rel. Grav., 43, 3079 (2011) · Zbl 1228.83097 · doi:10.1007/s10714-011-1225-3
[21] Chen, S.; Liu, X.; Liu, C.; Jing, J., No article title, Chin. Phys. Lett., 30, 060401 (2013) · doi:10.1088/0256-307X/30/6/060401
[22] Sheykhi, A., No article title, Phys. Rev. D, 86, 024013 (2012) · doi:10.1103/PhysRevD.86.024013
[23] Liang, J.; Sun, CB; Feng, HT, No article title, Europhys. Lett., 113, 30008 (2016) · doi:10.1209/0295-5075/113/30008
[24] Johnson, C.V: arXiv:1511.08782[hep-th] (2015)
[25] Witten, E., No article title, Adv. Theor. Math. Phys., 2, 253 (1998) · Zbl 0914.53048 · doi:10.4310/ATMP.1998.v2.n2.a2
[26] Maldacena, JM, No article title, Int. J. Theor. Phys., 38, 1113 (1999) · Zbl 0969.81047 · doi:10.1023/A:1026654312961
[27] Witten, E.: Adv. Theor. Math. Phys. 2 (1998)
[28] Dolan, BP, No article title, Class. Quant. Grav., 31, 035022 (2014) · Zbl 1285.83009 · doi:10.1088/0264-9381/31/3/035022
[29] Srednicki, M., No article title, Phys. Rev. Lett., 71, 666 (1993) · Zbl 0972.81649 · doi:10.1103/PhysRevLett.71.666
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.