Abstract
In this paper, we show that black holes with PMI source exhibit the \(T\)–\(S\) criticality and derive the relevant critical physical quantities analytically. The values of critical quantities for the case \(s\neq1\) vary from those for the case \(s=1\), showing the effect of PMI field on the critical phenomena of black holes. When \(q< q_{c}\), the \(T\)–\(S\) curve can be divided into three branches by a maximum point and a minimum point of Hawking temperature. With the help of specific heat analysis, we further show that the small entropy branch and the large entropy branch are stable. However, the medium entropy branch is unstable and can be removed via the technique of free energy analysis. Moreover, we examine the Maxwell equal area law and find that the relative errors for all the cases are small enough. So the existence of the PMI field does not affect the Maxwell equal area law.
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Acknowledgements
This research is supported by Special Funds for the Cultivation of Guangdong College Students’ Scientific and Technological Innovation (“Climbing Program” Special Funds) (Grant No. pdjh2017a0306) and supported by National Undergraduate Training Program for Innovation (Grant No. 201610579404). Gu-Qiang Li and Jie-Xiong Mo are also supported in part by National Natural Science Foundation of China (Grant No. 11605082), and Natural Science Foundation of Guangdong Province, China (Grant Nos. 2016A030307051, 2016A030310363, 2015A030313789).
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Lin, ZT., Li, GQ., Long, K. et al. \(T\)–\(S\) criticality of black holes with power Maxwell invariant source. Astrophys Space Sci 362, 162 (2017). https://doi.org/10.1007/s10509-017-3116-x
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DOI: https://doi.org/10.1007/s10509-017-3116-x