# Bardeen black hole surrounded by perfect fluid dark matter

• We derive an exact solution for a spherically symmetric Bardeen black hole surrounded by perfect fluid dark matter (PFDM). By treating the magnetic charge g and dark matter parameter $\alpha$ as thermodynamic variables, we find that the first law of thermodynamics and the corresponding Smarr formula are satisfied. The thermodynamic stability of the black hole is also studied. The results show that there exists a critical radius $r_{+}^{C}$ where the heat capacity diverges, suggesting that the black hole is thermodynamically stable in the range $0<r_{+}<r_{+}^{C}$ . In addition, the critical radius $r_{+}^{C}$ increases with the magnetic charge g and decreases with the dark matter parameter $\alpha$ . Applying the Newman-Janis algorithm, we generalize the spherically symmetric solution to the corresponding rotating black hole. With the metric at hand, the horizons and ergospheres are studied. It turns out that for a fixed dark matter parameter $\alpha$ , in a certain range, with the increase of the rotation parameter a and magnetic charge g, the Cauchy horizon radius increases while the event horizon radius decreases. Finally, we investigate the energy extraction by the Penrose process in a rotating Bardeen black hole surrounded by PFDM.
•  [1] Stephen W Hawking and George Francis Rayner Ellis, The large scale structure of space-time, volume 1. Cambridge University Press, 1973 [2] Stephen Hawking and Roger Penrose. The nature of space and time. Princeton University Press, 2010 [3] James M Bardeen, Non-singular general-relativistic gravitational collapse. In Proc. Int. Conf. GR5, Tbilisi, volume 174, 1968 [4] Eloy Ayón-Beato and Alberto Garcıa, Physics Letters B 493(1-2), 149-152 (2000 doi: 10.1016/S0370-2693(00)01125-4 [5] Eloy Ayon-Beato and Alberto Garcia, Physical Review Letters 80(23), 5056 (1998 doi: 10.1103/PhysRevLett.80.5056 [6] Sean A Hayward, Physical Review Letters 96(3), 031103 (2006 doi: 10.1103/PhysRevLett.96.031103 [7] Waldemar Berej, Jerzy Matyjasek, Dariusz Tryniecki et al., General Relativity and Gravitation 38(5), 885-906 (2006 doi: 10.1007/s10714-006-0270-9 [8] Andrei D Sakharov, Sov. Phys. JETP 22, 241-249 (1966 [9] Cao H Nam, General Relativity and Gravitation 50(6), 57 (2018 doi: 10.1007/s10714-018-2380-6 [10] Cosimo Bambi and Leonardo Modesto, Physics Letters B 721(4-5), 329-334 (2013 doi: 10.1016/j.physletb.2013.03.025 [11] Juliano CS Neves and Alberto Saa, Physics Letters B 734, 44-48 (2014 doi: 10.1016/j.physletb.2014.05.026 [12] Rahul Kumar, Sushant G Ghosh, and Anzhong Wang, Physical Review D 100(12), 124024 (2019 doi: 10.1103/PhysRevD.100.124024 [13] Sushant G Ghosh, Muhammed Amir, and Sunil D Maharaj, Nuclear Physics B, 115088 (2020 [14] Peter AR Ade, N Aghanim, M Arnaud et al., Astronomy and Astrophysics 594, A13 (2016 doi: 10.1051/0004-6361/201525830 [15] V V Kiselev, Classical and Quantum Gravity 20(6), 1187 (2003 doi: 10.1088/0264-9381/20/6/310 [16] Bobir Toshmatov, Zdeněk Stuchlík, and Bobomurat Ahmedov, The European Physical Journal Plus 132(2), 1-21 (2017 [17] Mahamat Saleh, Bouetou Bouetou Thomas, and Timoleon Crepin Kofane, International Journal of Theoretical Physics 57(9), 2640-2647 (2018 doi: 10.1007/s10773-018-3784-5 [18] Carlos A Benavides-Gallego, Ahmadjon Abdujabbarov, and Cosimo Bambi, Physical Review D 101(4), 044038 (2020 doi: 10.1103/PhysRevD.101.044038 [19] Sushant G Ghosh, Sunil D Maharaj, Dharmanand Baboolal et al., The European Physical Journal C 78(2), 1-8 (2018 [20] Yu Zhang and Y. X. Gui, Classical and Quantum Gravity 23(22), 6141 (2006 doi: 10.1088/0264-9381/23/22/004 [21] Sushant G Ghosh, The European Physical Journal C 76(4), 222 (2016 doi: 10.1140/epjc/s10052-016-4051-7 [22] Songbai Chen, Bin Wang, and Rukeng Su, Physical Review D 77(12), 124011 (2008 doi: 10.1103/PhysRevD.77.124011 [23] Ahmadjon Abdujabbarov, Bobir Toshmatov, Zdeněk Stuchlík et al., International Journal of Modern Physics D 26(06), 1750051 (2017 doi: 10.1142/S0218271817500511 [24] Mustapha Azreg-Aïnou and Manuel E Rodrigues, Journal of High Energy Physics 2013(9), 146 (2013 doi: 10.1007/JHEP09(2013)146 [25] V V Kiselev, Quintessential solution of dark matter rotation curves and its simulation by extra dimensions. arXiv: gr-qc/0303031, 2003 [26] Ming-Hsun Li and Kwei-Chou Yang, Physical Review D 86(12), 123015 (2012 doi: 10.1103/PhysRevD.86.123015 [27] Sumarna Haroon, Mubasher Jamil, Kimet Jusufi et al., Physical Review D 99(4), 044015 (2019 doi: 10.1103/PhysRevD.99.044015 [28] Xian Hou, Zhaoyi Xu, and Jiancheng Wang, Journal of Cosmology and Astroparticle Physics 2018(12), 040 (2018 doi: 10.1088/1475-7516/2018/12/040 [29] Zhaoyi Xu, Xian Hou, and Jiancheng Wang, Classical and Quantum Gravity 35(11), 115003 (2018 doi: 10.1088/1361-6382/aabcb6 [30] Zhaoyi Xu, Xian Hou, Xiaobo Gong et al., The European Physical Journal C 78(6), 513 (2018 doi: 10.1140/epjc/s10052-018-5991-x [31] Muhammad Rizwan, Mubasher Jamil, and Kimet Jusufi, Physical Review D 99(2), 024050 (2019 doi: 10.1103/PhysRevD.99.024050 [32] Leonardo Balart and Sharmanthie Fernando, Modern Physics Letters A 32(39), 1750219 (2017 doi: 10.1142/S0217732317502194 [33] Rong-Gen Cai, Li-Ming Cao, Li Li et al., Journal of High Energy Physics 2013(9), 5 (2013 doi: 10.1007/JHEP09(2013)005 [34] Zhaoyi Xu, Xian Hou, Jiancheng Wang et al., Advances in High Energy Physics, 2019 (2019 [35] Shao-Wen Wei and Yu-Xiao Liu, Physical Review D 101(10), 104018 (2020 doi: 10.1103/PhysRevD.101.104018 [36] Ezra T Newman and AI Janis, Journal of Mathematical Physics 6(6), 915-917 (1965 doi: 10.1063/1.1704350 [37] Bobir Toshmatov, Zdeněk Stuchlík, and Bobomurat Ahmedov, Physical Review D 95(8), 084037 (2017 doi: 10.1103/PhysRevD.95.084037 [38] Rahul Kumar and Sushant G Ghosh, The European Physical Journal C 78(9), 750 (2018 doi: 10.1140/epjc/s10052-018-6206-1 [39] Zhaoyi Xu and Jiancheng Wang, Physical Review D 95(6), 064015 (2017 doi: 10.1103/PhysRevD.95.064015 [40] Zhaoyi Xu, Xiaobo Gong, and Shuang-Nan Zhang, Physical Review D 101(2), 024029 (2020 doi: 10.1103/PhysRevD.101.024029 [41] Rajibul Shaikh, Physical Review D 100(2), 024028 (2019 doi: 10.1103/PhysRevD.100.024028 [42] Hyeong-Chan Kim, Bum-Hoon Lee, Wonwoo Lee et al., Physical Review D 101(6), 064067 (2020 doi: 10.1103/PhysRevD.101.064067 [43] Kimet Jusufi, Mubasher Jamil, Hrishikesh Chakrabarty et al., Physical Review D 101(4), 044035 (2020 doi: 10.1103/PhysRevD.101.044035 [44] Mustapha Azreg-Aïnou, Sumarna Haroon, Mubasher Jamil et al., International Journal of Modern Physics D 28(04), 1950063 (2019 doi: 10.1142/S0218271819500639 [45] Cheng Liu, Tao Zhu, Qiang Wu et al., Physical Review D 101(8), 084001 (2020 doi: 10.1103/PhysRevD.101.084001 [46] Mustapha Azreg-Aïnou, Physical Review D 90(6), 064041 (2014 doi: 10.1103/PhysRevD.90.064041 [47] Mustapha Azreg-Aïnou, The European Physical Journal C 74(5), 2865 (2014 doi: 10.1140/epjc/s10052-014-2865-8 [48] Robert M Wald. General Relativity. University of Chicago Press, 2010 [49] Sumarna Haroon, Mubasher Jamil, Kai Lin, Petar Pavlovic et al., The European Physical Journal C 78(6), 519 (2018 doi: 10.1140/epjc/s10052-018-5986-7 [50] Parthapratim Pradhan, The European Physical Journal C 79(5), 1-16 (2019 [51] Sourav Bhattacharya, Physical Review D 97(8), 084049 (2018 doi: 10.1103/PhysRevD.97.084049 [52] Kazunori Akiyama, Antxon Alberdi, Walter Alef et al., The Astrophysical Journal Letters 875(1), L4 (2019 doi: 10.3847/2041-8213/ab0e85 [53] Zdenek Stuchlík and Jan Schee, The European Physical Journal C 79(1), 1-13 (2019 doi: 10.1140/epjc/s10052-018-6506-5 [54] Peng-Zhang He, Qi-Qi Fan, Hao-Ran Zhang et al., The European Physical Journal C 80(12), 1-13 (2020 [55] He-Xu Zhang, Cong Li, Peng-Zhang He et al., European Physical Journal C 80(5), 1-11 (2020

Figures(9)

Get Citation
He-Xu Zhang, Yuan Chen, Tian-Chi Ma, Peng-Zhang He and Jian-Bo Deng. Bardeen black hole surrounded by perfect fluid dark matter[J]. Chinese Physics C. doi: 10.1088/1674-1137/abe84c
He-Xu Zhang, Yuan Chen, Tian-Chi Ma, Peng-Zhang He and Jian-Bo Deng. Bardeen black hole surrounded by perfect fluid dark matter[J]. Chinese Physics C.
Milestone
Article Metric

Article Views(105)
Cited by(0)
Policy on re-use
To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.
###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

Title:
Email:

## Bardeen black hole surrounded by perfect fluid dark matter

###### Corresponding author: Jian-Bo Deng, dengjb@lzu.edu.cn
• Institute of Theoretical Physics & Research Center of Gravitation, Lanzhou University, Lanzhou 730000, China

Abstract: We derive an exact solution for a spherically symmetric Bardeen black hole surrounded by perfect fluid dark matter (PFDM). By treating the magnetic charge g and dark matter parameter $\alpha$ as thermodynamic variables, we find that the first law of thermodynamics and the corresponding Smarr formula are satisfied. The thermodynamic stability of the black hole is also studied. The results show that there exists a critical radius $r_{+}^{C}$ where the heat capacity diverges, suggesting that the black hole is thermodynamically stable in the range $0<r_{+}<r_{+}^{C}$ . In addition, the critical radius $r_{+}^{C}$ increases with the magnetic charge g and decreases with the dark matter parameter $\alpha$ . Applying the Newman-Janis algorithm, we generalize the spherically symmetric solution to the corresponding rotating black hole. With the metric at hand, the horizons and ergospheres are studied. It turns out that for a fixed dark matter parameter $\alpha$ , in a certain range, with the increase of the rotation parameter a and magnetic charge g, the Cauchy horizon radius increases while the event horizon radius decreases. Finally, we investigate the energy extraction by the Penrose process in a rotating Bardeen black hole surrounded by PFDM.

Reference (55)

/