标题： 广义相对论中Bardeen黑洞的热力学性质 显示英文标题

标题： Thermodynamic properties of Bardeen black holes in dRGT massive gravity

摘要： 巴德金黑洞解是基于萨哈罗夫和格林纳提议的第一个球对称的正则黑洞，这是对施瓦茨希尔德黑洞的修改。 我们在存在德·拉姆、加巴达德泽和托利（dRGT）大质量引力的情况下呈现巴德金黑洞解，该解在非线性源存在的情况下在所有地方都是正则的。 获得的解在没有大质量引力参数时退化为巴德金黑洞，在磁荷$g = 0$时退化为施瓦茨希尔德黑洞。 我们研究了热力学量，即质量（M）、温度$(T)$、熵（$S$）和自由能$(F)$，根据视界半径在正则系综和巨正则系综中进行分析。 我们通过研究比热容和自由能来检查所获得解的局部和全局稳定性。 比热容在$r = r_c$处改变符号。 黑洞具有正比热容$C > 0$（即，自由能$F < 0$为负值，全局优选）。 此外，我们在两种系综中研究了所获得解的相结构。 显示英文摘要

摘要： The Bardeen black hole solution is the first spherically symmetric regular black hole based on the Sakharov and Gliner proposal which is a modification of the Schwarzschild black hole. We present the Bardeen black hole solution in the presence of the de Rham, Gabadaadze, and Tolly (dRGT) massive gravity, which is regular everywhere in the presence of a nonlinear source. The obtained solution reduces to the Bardeen black hole in the absence of a massive gravity parameter, and the Schwarzschild black hole when magnetic charge $g = 0$. We investigated the thermodynamic quantities, that is, mass (M), temperature $(T)$, entropy ($S$), and free energy $(F)$, in terms of the horizon radius for both canonical and grand canonical ensembles. We checked the local and global stability of the obtained solution by studying the heat capacity and free energy. The heat capacity changes sign at $r = r_c$. The black hole is thermodynamically stable with a positive heat capacity $C > 0$ (i.e., globally preferred with negative free energy $F < 0$). In addition, we studied the phase structure of the obtained solution in both ensembles.