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arXiv 2009.05904gr-qc
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Euler-Heisenberg-AdS黑洞的热力学

Thermodynamics of the Euler-Heisenberg-AdS black hole

Daniela Magos, Nora Bretón

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18 pages, 11 figures
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摘要：

我们推广的解决方案的欧拉-海森堡（EH）理论耦合到引力，代表一个非线性带电的静态黑洞（BH）引入宇宙学常数，得到的解决方案的特点是由四个参数：质量$M$，电荷$Q$，宇宙学常数$Λ$（正或负）和欧拉-海森堡理论参数$a$。然后简要分析了BH的一些特征，如层位、电磁场和测地线。我们主要关注它的热力学性质在扩展的空间中的anti-de Sitter参数解释为压力;我们显示Smarr公式和BH热力学第一定律之间的一致性，解释的参数EH理论的真空极化。我们确定的状态方程和临界点;临界体积确定两个分支的BH，一个接近麦克斯韦行为和第二个明显的非线性电磁。此外，Gibbs自由能分析表明，BH可以发生两个相变;我们还构造了共存曲线$P$ - $T$，在此可以观察到BH的不同相;临界点由标准平均场理论指数表征，临界变量满足$P_{\rm crit} v_{\rm crit}/ T_{\rm crit} = 3/8 $加上Euler-Heisenberg参数$a$中的万分之一阶项

英文摘要：

We generalize the solution to the Euler-Heisenberg (EH) theory coupled to gravity that represents a nonlinearly charged static black hole (BH) introducing the cosmological constant; the obtained solution is characterized by four parameters: mass $M$, electric charge $Q$, cosmological constant $Λ$ (positive or negative) and the Euler-Heisenberg theory parameter $a$. Then we briefly analyze some BH features like horizons, electromagnetic field and geodesics. We mainly focus on its thermodynamic properties in the extended space where the anti-de Sitter parameter is interpreted as the pressure; we show the consistency between the Smarr formula and the first law of BH thermodynamics, interpreting the parameter of the EH theory as the vacuum polarization. We determine the equation of state and the critical points; the critical volume determines two branches of BHs, one near Maxwell behavior and a second one manifestly nonlinear electromagnetic. Moreover, the analysis of the Gibbs free energy indicates that two phase transitions can occur; we also construct the coexistence curve $P$-$T$ where the different phases of the BH can be observed; the critical point is characterized by the standard mean field theory exponents, and the critical variables satisfy $P_{\rm crit} v_{\rm crit}/ T_{\rm crit} = 3/8 $ plus terms of the ten thousandths order in the Euler-Heisenberg parameter $a$

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