Document Type : Original Article
Authors
1. Department of Physics,School of Science, Shiraz University, Shiraz, Iran 2. Biruni Observatory, School of Science, Shiraz University, Shiraz, Iran
Abstract
In this paper, asymptotically AdS black hole solutions of massive gravity in the presence of nonlinear electromagnetic field arisen from the power theory of Maxwell invariant are investigated and the associated Euclidean on-shell action is presented. Using the Euclidean on-shell action, the gravitational partition function in the canonical ensemble is computed in arbitrary dimensions and then thermodynamic quantities of topological black holes are obtained. By extending the thermodynamic phase space, i.e., treating negative cosmological constant as thermodynamic pressure, the first law of thermodynamics as well as associated Smarr formula are examined. Next, the equation of state of topological black holes is obtained and it is proven that the critical point equation of these solutions can exhibit black hole phase transitions similar to those of van der Waals, van der Waals like and solid/liquid/gas (related to triple point) phase transitions in usual thermodynamic systems. Especially, the van der Waals phase transition is observed in 4 and higher dimensions, van der Waals type phase transition can be seen in 6 and higher dimensions, and phase transitions associated with triple point, i.e., small/intermediate/large black hole phase transition may happen in 6 and higher dimensions.
Keywords
- D Kastor, S Ray, and J Traschen, Class. Quant. Grav. 26 (2009) 195011.
- B P Dolan, Phys. Rev. D 84 (2011) 127503.
- D Kubiznak, R B Mann, and M Teo, Class. Quant. Grav. 34 (2017) 063001.
- A Chamblin, R Emparan, C V Johnson, and R C Myers, Phys. Rev. D 60 (1999) 104026.
- Chamblin, R Emparan, C V Johnson, and R C Myers, Phys. Rev. D 60 (1999) 064018.
- D Kubiznak and R B Mann, JHEP 07 (2012) 033.
- N Altamirano, D Kubiznak, and R B Mann, Phys. Rev. D 88 (2013) 101502.
- S Gunasekaran, R B Mann, and D Kubiznak, JHEP 11 (2012) 110.
- N Altamirano, D Kubiznak, R B Mann, and Z Sherkatghanad, Class. Quant. Grav. 31 (2014) 042001.
10. J X Mo and W B Liu, EPJC 74 (2014) 2836.
11. A M Frassino, D Kubiznak, R B Mann, and F Simovic, JHEP 09 (2014) 080.
12. R A Hennigar, JHEP 09 (2017) 082.
13. S H Hendi, R B Mann, S Panahiyan, and B Eslam Panah, Phys. Rev. D 95 (2017) 021501(R).
14. D Zou, R Yue, and M Zhang, EPJC 77 (2017) 256.
15. M Zhang, D Zou, and R Yue, Adv. High Energy Phys. 2017 (2017) 3819246.
16. Z Sherkatghanad, B Mirza, Z Mirzaeyan, and S A H Mansoori, Int. J. Mod. Phys. D 26 (2014) 1750017.
17. J Xu, L M Cao, and Y P Hu, Phys. Rev. D 91 (2015) 124033.
18. B Mirza and Z Sherkatghanad, Phys. Rev. D 90 (2014) 084006.
19. R A Hennigar, W G Brenna, and R B Mann, JHEP 07 (2015) 077.
20. R G Cai, L M Cao, L Li, and R Q Yang, JHEP 09 (2013) 005.
21. D Zou, Y Liu, and B Wang, Phys. Rev. D 90 (2014) 044063.
22. S Wei and Y Liu, Phys. Rev. D 87 (2013) 044014.
23. W Xu, H Xu, and L Zhao, EPJC 74 (2014) 2970.
24. S H Hendi, S Panahiyan, S Upadhyay, and B Eslam Panah, Phys. Rev. D 95 (2017) 084036.
25. S H Hendi and A Dehghani, EPJC 79 (2019) 227.
26. A Dehyadegari, M K Zangeneh, and A Sheykhi, Phys. Lett. B 773 (2017) 344.
27. S H Hendi, B Eslam Panah, and S Panahiyan, Fortschr. Phys. (Prog. Phys.) 2018 (2018) 1800005.
28. C de Rham and G Gabadadze, Phys. Rev. D 82 (2010) 044020.
29. C de Rham, G Gabadadze, and A J Tolley, Phys. Rev. Lett. 106 (2011) 231101.
30. D Vegh, Holography without translational symmetry, arXiv: 1301.0537
31. R G Cai, Y P Hu, Q Y Pan, and Y L Zhang, Phys. Rev. D 91 (2015) 024032.
32. S H Hendi, S Panahiyan, and B Eslam Panah, JHEP 01 (2016) 129.
33. S F Hassan and R A Rosen, Phys. Rev. Lett. 108 (2012) 041101.
34. L Alberte and A Khmelnitsky, Phys. Rev. D 88 (2013) 064053.
35. M Blake and D Tong, Phys. Rev. D 88 (2013) 106004.
36. R A Davison, Phys. Rev. D 88 (2013) 086003.
37. J B Jiménez, L Heisenberg, G J Olmo, and D Rubiera-Garcia, Phys. Rep. 727 (2018) 1.
38. V I Afonso, G I Olmo, E Orazi, and D Rubiera-Garcia, EPJC 78 (2018) 866.
39. L Alberte and A Khmelnitsky, Phys. Rev. D 91 (2015) 046006.
40. T Matsubara, Prog. Theor. Phys. 14 (1955) 351.
41. J M Bardeen, B Carter, and S W Hawking, Commun. Math. Phys. 31 (1973) 161.
42. G W Gibbons, S W Hawking, Phys. Rev. D 15 (1977) 2752.
43. G ’t Hooft, M Veltman, Ann. Phys. Theor. A 20 (1974) 69.
44. P Kraus, F Larsen, and R Siebelink, Nucl. Phys. B 563 (1999) 259.
45. S Hawking and D N Page, Commun. Math. Phys. 87 (1983) 577.
46. E Witten, Adv. Theor. Math. Phys. 2 (1998) 505.
47. D J Brown and J W York, Phys. Rev. D 47 (1993) 1407.
48. A Dehghani, S H Hendi, and R B Mann, Phys. Rev. D 101 (2020) 084026.
49. S W Wei and Y X Liu, Phys. Rev. D 90 (2014) 044057.
50. S W Wei and Y X Liu, Phys. Rev. Lett. 115 (2015) 111302.