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arXiv 2209.09031hep-thgr-qc
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五维带电旋转黑洞的热力学:一种反项处理方法

Thermodynamics of 5D Charged Rotating Black Holes: A Counterterms Treatment

Adel Awad, Hassan ElSayed

AI总结:

针对五维带电旋转黑洞,本文用反项法计算体与边界热力学量,并推广热力学体积定义以纳入共形异常,恢复扩展相空间中的第一定律与Smarr关系。

摘要:

我们证明,体理论中热力学体积的计算对偶CFT中的共形异常很敏感,并提出了一种在共形异常不消失时计算该体积的新方法。这解决了使用反项减去法似乎会破坏扩展相空间中第一定律和Smarr关系的问题。我们以五维最小规范超引力中的带电旋转黑洞(Chong等人,Phys Rev Lett 95:161301, 2005)为例明确展示了这一点,其中我们使用反项法研究该解的热力学。在使用反项法计算的体量中,包括该解的在壳作用量、总质量和角动量。所有这些量都与先前使用其他方法进行的计算一致。对于边界CFT,我们计算了重整化应力张量、共形异常和Casimir能量。利用Papadimitriou-Skenderis分析(Papadimitriou和Skenderis,J. High Energy Phys. 08:004, 2005),我们证明通过反项法计算的质量满足黑洞热力学第一定律。为讨论扩展热力学,我们采用类似于Papadimitriou-Skenderis的程序,将热力学体积的定义推广到存在共形异常的情形。我们证明该体积正确计入了由边界度规变分产生的额外项。

英文摘要:

We show that the calculation of the thermodynamic volume in the bulk theory is sensitive to conformal anomalies in the dual CFT, and present a new way of calculating it when the conformal anomalies do not vanish. This solves the issue where the use of the counterterms subtraction method appears to break the first law and Smarr's relation in extended phase-space. This is shown explicitly in the case of charged rotating black holes in five-dimensional minimal gauged supergravity (Chong et al. in Phys Rev Lett 95:161301, 2005), where we use the counterterms method to study the thermodynamics of the solution. Among the bulk quantities calculated using the counterterms method are the on-shell action, total mass, and angular momenta of the solution. All these quantities are consistent with previous calculations made using other methods. For the boundary CFT, we calculate the renormalized stress tensor, conformal anomaly, and Casimir energy. Using the Papadimitriou-Skenderis analysis (Papadimitriou and Skenderis in J. High Energy Phys. 08:004, 2005), we show that the mass calculated via the counterterms method satisfies the first law of black hole thermodynamics. To discuss extended thermodynamics, we extend the definition of the thermodynamic volume to cases with conformal anomalies using a procedure similar to that of Papadimitriou-Skenderis. We show that this volume correctly accounts for extra terms due to boundary metric variation.

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