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arXiv 1310.3286hep-thgr-qc
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磁化Kerr-Newman黑洞的热力学

Thermodynamics of Magnetised Kerr-Newman Black Holes

G. W. Gibbons, Yi Pang, C. N. Pope

备注：
27 pages
发表信息：
Phys. Rev. D 89, 044029 (2014)
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摘要：

研究了附加磁场$B$中磁化Kerr-Newman黑洞的各阶热力学性质.度规场和其他场的渐近性质主要由沿轴向无限延伸的磁通量决定，这导致了计算守恒量（如角动量和质量）的微妙之处。我们提出了一个详细的讨论的实施的Wald型程序来计算角动量，显示如何模糊，是不存在的通常的渐近平坦的情况下，可以解决规范不变性的要求。我们还提出了一种形式主义，从中我们能够获得的磁化黑洞的质量的表达式。质量和角动量的表达式与热力学热力学第一定律和Smarr型关系相容。允许附加磁场$B$变化导致形式为$-μdB$的第一定律中的额外项，其中$μ$被解释为感应磁矩。最小化的总能量相对于总电荷$Q$在固定值的角动量和能量的种子度量允许调查沃尔德的过程。迈斯纳效应被证明对电中性极端黑洞成立。在四维STU模型中，我们给出了黑洞角动量的一个推导，该模型是${\cal N}=2$超引力耦合到三个矢量多重态。

英文摘要：

The thermodynamics of a magnetised Kerr-Newman black hole is studied to all orders in the appended magnetic field $B$. The asymptotic properties of the metric and other fields are dominated by the magnetic flux that extends to infinity along the axis, leading to subtleties in the calculation of conserved quantities such as the angular momentum and the mass. We present a detailed discussion of the implementation of a Wald-type procedure to calculate the angular momentum, showing how ambiguities that are absent in the usual asymptotically-flat case may be resolved by the requirement of gauge invariance. We also present a formalism from which we are able to obtain an expression for the mass of the magnetised black holes. The expressions for the mass and the angular momentum are shown to be compatible with the first law of thermodynamics and a Smarr type relation. Allowing the appended magnetic field $B$ to vary results in an extra term in the first law of the form $-μdB$ where $μ$ is interpreted as an induced magnetic moment. Minimising the total energy with respect to the total charge $Q$ at fixed values of the angular momentum and energy of the seed metric allows an investigation of Wald's process. The Meissner effect is shown to hold for electrically neutral extreme black holes. We also present a derivation of the angular momentum for black holes in the four-dimensional STU model, which is ${\cal N}=2$ supergravity coupled to three vector multiplets.

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