Born-Infeld型非线性电动力学黑洞的$P-V$临界性和几何热力学
$P-V$ criticality and geometrothermodynamics of black holes with Born-Infeld type nonlinear electrodynamics
摘要：
在本文中，我们考虑了具有对数和指数形式的非线性电动力学的爱因斯坦引力的黑洞解。我们把$Λ$看作一个动力学压力来研究黑洞与范德华系统的类比。我们绘制了正则系综中adS黑洞的P-v图、T-v图和G-T图，研究了正则系综中adS黑洞的相变.我们研究电动力学的非线性效应，看看非线性的力量如何影响临界行为。我们还研究了维度对临界值的影响，并分析了它的关键作用。此外，我们显示了不同参数变化时通用比率P_{c} v_{c} / T_{c}的变化。此外，我们还对线性和非线性电动力学作了比较，指出最低临界温度属于麦克斯韦理论。此外，我们提出了一些参数，关于如何权力的非线性带来的系统Schwarzschild和Reissner-Nordstrom的限制。接下来，我们在热容的背景下研究临界行为。我们证明了系统的临界行为与扩展相空间相图中的临界行为相似。指出了扩展相空间的相变点只表现为热容的发散。我们还利用GTD方法扩展了对相变的研究。我们引入了两个新的度量，并证明了新度量的TRS发散与相变相一致。这些发散的特征行为，即临界点，正是在扩展的相空间和热容中得到的。本文还介绍了一种考虑热容分母的临界压力和视界半径的新方法。我们表明，有几个好处，使这种方法有利相比，其他的。
英文摘要：
In this paper, we take into account the black hole solutions of Einstein gravity with logarithmic and exponential forms of nonlinear electrodynamics. We consider $Λ$ as a dynamical pressure to study the analogy of the black holes with the Van der Waals system. We plot P-v, T-v and G-T diagrams and investigate the phase transition of adS black holes in the canonical ensemble. We study the nonlinearity effects of electrodynamics and see how the power of nonlinearity affects critical behavior. We also investigate the effects of dimensionality on the critical values and analyze its crucial role. Moreover, we show the changes in the universal ratio P_{c}v_{c}/T_{c} for variation of different parameters. In addition, we make a comparison between linear and nonlinear electrodynamics and show that the lowest critical temperature belongs to Maxwell theory. Also, we make some arguments regarding to how power of nonlinearity brings the system to Schwarzschild-like and Reissner-Nordstrom-like limitations. Next, we study the critical behavior in context of heat capacity. We show that critical behavior of system is similar to one in phase diagrams of extended phase space. We point out that phase transition points of the extended phase space only appear as divergencies of heat capacity. We also extend the study of phase transitions through GTD method. We introduce two new metrics and show that divergencies of TRS of the new metrics coincide with phase transitions. The characteristic behavior of these divergencies, hence critical points is exactly the one that is obtained in extended phase space and heat capacity. We also introduce a new method for obtaining critical pressure and horizon radius by considering denominator of the heat capacity. We show that there are several benefits that make this approach favorable comparing to other ones.
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