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首页> 外文期刊>Physical review, D >Critical behavior of Lifshitz dilaton black holes
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Critical behavior of Lifshitz dilaton black holes

机译：Lifshitz dilaton黑洞的临界行为

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Until now, the critical behavior of Lifshitz black holes, in an extended P ? v space, has not been studied, because it is impossible to find an analytical equation of state, P = P ( v , T ) , for an arbitrary Lifshitz exponent z . In this paper, we adopt a new approach toward thermodynamic phase space and successfully explore the critical behavior of ( n + 1 )-dimensional Lifshitz dilaton black holes. The most important advantage of this approach is that we keep the cosmological constant as a constant without needing to vary it. For this purpose, we write down the equation of state as Q s = Q s ( T , Ψ ) , where Ψ = ( ? M / ? Q s ) S , P is the conjugate of Q s , and construct a Smarr relation based on this new phase space as M = M ( S , Q s , P ) , where s = 2 p / ( 2 p ? 1 ) , with p the power of the power-law Maxwell Lagrangian. We justify such a choice mathematically and show that with this new phase space, the system admits the critical behavior and resembles the van der Waals fluid system when the cosmological constant (pressure) is treated as a fixed parameter, while the charge of the system varies. We obtain the Gibbs free energy of the system and find a swallowtail shape in Gibbs diagrams, which represents the first-order phase transition. Finally, we calculate the critical exponents and show that although thermodynamic quantities depend on the metric parameters such as z , p , and n , the critical exponents are the same as the van der Waals fluid-gas system. This alternative viewpoint of the phase space of a Lifshitz dilaton black hole can be understood easily since one can imagine such a change for a given single black hole, i.e., acquiring charge, which induces the phase transition. Our results further support the viewpoint suggested in [A. Dehyadegari, A. Sheykhi, and A. Montakhab, Phys. Lett. B 768 , 235 (2017)].
机译：到现在为止，Lifshitz黑洞的临界行为在扩展的P？ v空间尚未进行研究，因为对于任意Lifshitz指数z不可能找到状态解析方程P = P（v，T）。在本文中，我们对热力学相空间采用了一种新方法，并成功地探索了（n +1）维Lifshitz dilaton黑洞的临界行为。这种方法最重要的优点是我们无需改变就可以保持宇宙常数不变。为此，我们将状态方程写为Q s = Q s（T，Ψ），其中Ψ=（？M /？Q s）S，P是Q s的共轭，并构造一个基于Smarr关系的在这个新的相空间上，M = M（S，Q s，P），其中s = 2 p /（2 p？1），其中p为幂律麦克斯韦拉格朗日函数的幂。我们用数学方法证明了这种选择的合理性，并表明在这种新的相空间下，当宇宙常数（压力）被视为固定参数时，系统可以接受临界行为，并且类似于范德华流体系统，而系统的电荷却在变化。我们获得了系统的吉布斯自由能，并在吉布斯图中找到了燕尾形状，该形状代表一阶相变。最后，我们计算了临界指数，并表明尽管热力学量取决于度量参数，例如z，p和n，但临界指数与Van der Waals流体-气体系统相同。 Lifshitz dilaton黑洞的相空间的这种替代观点很容易理解，因为人们可以想象给定的单个黑洞的这种变化，即获取电荷，从而引起相变。我们的结果进一步支持了[A. Dehyadegari，A。Sheykhi和A.Montakhab，物理学。来吧B 768，235（2017）]。

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