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The $P$–$v$ Criticality of a Noncommutative Geometry-Inspired Schwarzschild-AdS Black Hole |
| Jun Liang** |
School of Arts and Sciences, Shaanxi University of Science and Technology, Xi'an 710021
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| Cite this article: |
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Jun Liang 2017 Chin. Phys. Lett. 34 080402 |
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Abstract The $P$–$v$ criticality and phase transition in the extended phase space of a noncommutative geometry-inspired Schwarzschild black hole in anti-de Sitter (AdS) spacetime are studied. The cosmological constant is treated as a dynamical pressure and its conjugate quantity is thermodynamic volume of the noncommutative geometry-inspired Schwarzschild-AdS black hole. The noncommutative parameter is also treated as a variable, and as a consequence, a new thermodynamic quantity $V_{\theta}$ conjugate to $P_{\theta}=-(8\pi \theta)^{-1}$ has to be defined further, which is required for consistency of both the first law of thermodynamics and the corresponding Smarr relation. We find that the $P$–$v$ criticality and the small black hole/large black hole phase transition appear for the noncommutative Schwarzschild-AdS black hole. Numerical calculations indicate that the noncommutative parameter $\theta$ affects the phase transition as well as the critical temperature $T_{\rm c}$, horizon radius $r_{\rm +c}$ and pressure $P_{\rm c}$. However, the critical ratio $P_{\rm c}r_{\rm +c}/T_{\rm c}$ is universal (independent of $\theta$), which is very similar to the result in the van de Waals liquid–gas system, but different from that in the noncommutative geometry-inspired Reissner–Nordström-AdS black hole, where the critical ratio is no longer universal.
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Received: 31 March 2017
Published: 22 July 2017
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| PACS: |
04.70.-s
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(Physics of black holes)
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04.70.Dy
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(Quantum aspects of black holes, evaporation, thermodynamics)
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05.70.Ce
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(Thermodynamic functions and equations of state)
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| Fund: Supported by the Natural Science Foundation of Education Department of the Shaannxi Province under Grant No 15JK1077, and the Doctorial Scientific Research Starting Fund of Shaannxi University of Science and Technology under Grant No BJ12-02. |
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| [1] | Kubizňák D and Mann R B 2012 J. High Energy Phys. 1207 033 | | [2] | Kastor D, Ray S and Traschen J 2009 Class. Quantum Grav. 26 195011 | | [3] | Gunasekaran S, Mann R B and Kubizňák D 2012 J. High Energy Phys. 1211 110 | | [4] | Cai R G et al 2012 J. High Energy Phys. 1209 005 | | [5] | Hendi S H and Vahidinia M H 2013 Phys. Rev. D 88 084045 | | [6] | Belhaj A et al 2012 Chin. Phys. Lett. 29 100401 | | [7] | Chen S et al 2013 Chin. Phys. Lett. 30 060401 | | [8] | Zhao R et al 2013 Eur. Phys. J. C 73 2645 | | [9] | Altamirano N, Kubizňák D and Mann R B 2013 Phys. Rev. D 88 101502 | | [10] | Mo J X and Liu W B 2013 Phys. Lett. B 727 336 | | [11] | Spallucci E and Smailagic A 2013 Phys. Lett. B 723 436 | | [12] | Altamirano N et al 2014 Galaxies 2 89 | | [13] | Altamirano N et al 2014 Class. Quantum Grav. 31 042001 | | [14] | Wei S W and Liu Y X 2014 Phys. Rev. D 90 044057 | | [15] | Xu W, Xu H and Zhao L 2014 Eur. Phys. J. C 74 2970 | | [16] | Zou C D, Zhang S J and Wang B 2014 Phys. Rev. D 89 044002 | | [17] | Mo J X and Liu W B 2014 Eur. Phys. J. C 74 2836 | | [18] | Zhang L C et al 2014 Eur. Phys. J. C 74 3052 | | [19] | Mo J X and Liu W B 2014 Phys. Rev. D 89 084057 | | [20] | Zou C D, Liu Y and Wang B 2014 Phys. Rev. D 90 044063 | | [21] | Zhao Z and Jing J 2014 J. High Energy Phys. 1411 037 | | [22] | Zhao R et al 2014 Adv. High Energy Phys. 2014 124854 | | [23] | Xu H, Xu W and Zhao L 2014 Eur. Phys. J. C 74 3074 | | [24] | Frassino A M et al 2014 J. High Energy Phys. 1409 080 | | [25] | Li G Q 2014 Phys. Lett. B 735 256 | | [26] | Dolan B P et al 2014 Class. Quantum Grav. 31 242001 | | [27] | Zhang J L, Cai R G and Yu H 2015 J. High Energy Phys. 1502 143 | | [28] | Rajagopal A, Kubizňák D and Mann R B 2014 Phys. Lett. B 737 277 | | [29] | Liu Y, Zou C D and Wang B 2014 J. High Energy Phys. 1409 179 | | [30] | Dolan B P 2014 Phys. Rev. D 90 084002 | | [31] | Wei S W and Liu Y X 2015 Phys. Rev. D 91 044018 | | [32] | Hennigar R A, Brenna W G and Mann R B 2015 J. High Energy Phys. 1507 077 | | [33] | Xu J, Cao L M and Hu Y P 2015 Phys. Rev. D 91 124033 | | [34] | Liang J, Sun C B and Feng H T 2016 Europhys. Lett. 113 30008 | | [35] | Liang J et al 2017 Gen. Relativ. Gravitation 49 29 | | [36] | Frassino A M 2016 Springer. Proc. Phys. 170 241 | | [37] | Nicolini P, Smailagic A and Spallucci E 2006 Phys. Lett. B 632 547 | | [38] | Banerjee R et al 2008 Phys. Rev. D 77 124035 |
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