In this work, we study thermodynamics of generalized Ayon-Beato and Garcia (ABG) black hole metric which contains three parameters named as mass , magnetic charge , and dimensionless coupling constant of nonlinear electrodynamics interacting field . We showed that central regions of this black hole behaves as dS (AdS) vacuum space by setting and in the case reaches to a flat Minkowski space. In the large distances, this black hole behaves as a Reissner-Nordstrom BH. However, an important role of the charge appeared in the production of a formal variable cosmological parameter which will support pressure coordinate in the thermodynamic perspective of this black hole in our setup. We should point that this formal variable cosmological parameter is different with cosmological constant which comes from AdS/CFT correspondence, and it is effective at large distances as AdS space pressure. In our setup, the assumed pressure originated from the internal material of the black hole say and here. By calculating the Hawking temperature of this black hole, we obtain equation of state. Then, we plotted isothermal P-V curves and heat capacity at constant pressure. They show that the system participates in the small to large phase transition of the black hole or the Hawking-Page phase transition which is similar to the van der Waals phase transition in the ordinary thermodynamics systems. In fact in the Hawking-Page phase transition disequilibrium, evaporating generalized ABG black hole reaches to a vacuum AdS space finally.

中文翻译：

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广义 Ayon-Beato Garcia 黑洞的热力学相变

在这项工作中，我们研究了广义 Ayon-Beato 和 Garcia (ABG) 黑洞度量的热力学，该度量包含三个参数，即质量、磁荷和非线性电动力学相互作用场的无量纲耦合常数。我们通过设置表明这个黑洞的中心区域表现为 dS (AdS) 真空空间在这种情况下达到平坦的 Minkowski 空间。在远距离上，这个黑洞表现为 Reissner-Nordstrom BH。然而，电荷的一个重要作用出现在一个正式的可变宇宙学参数的产生中，该参数将支持我们设置中这​​个黑洞的热力学观点中的压力坐标。需要指出的是，这个形式变量宇宙学参数不同于来自 AdS/CFT 对应的宇宙学常数，它作为 AdS 空间压力在远距离有效。在我们的设置中，假设的压力来自黑洞的内部物质，比如这里。通过计算这个黑洞的霍金温度，我们得到了状态方程。然后，我们绘制了恒压下的等温 PV 曲线和热容量。他们表明系统参与了黑洞从小到大的相变或类似于普通热力学系统中范德瓦尔斯相变的霍金-佩奇相变。事实上在霍金-佩奇相变不平衡中，蒸发的广义 ABG 黑洞最终到达真空 AdS 空间。