arXiv 0704.07292007-04-10hep-th

提升Kaluza-Klein黑洞的第一定律

The First Law for Boosted Kaluza-Klein Black Holes

David Kastor, Sourya Ray, Jennie Traschen

备注：: 20 pages, 0 figures; v2 - reference added
发表信息：: JHEP 0706:026,2007
DOI：: 10.1088/1126-6708/2007/06/026

摘要：

研究了具有沿紧维动量但角动量为零的Kaluza-Klein黑洞的热力学性质。这些黑洞是静止的，但不旋转。我们推导出这些时空的第一定律，并发现与紧致方向长度变化共轭的参数是一个有效张力，它通常不同于ADM张力。对于增强的黑弦，该有效张力总是正的，而对于大的增强参数，ADM张力是负的。我们还推导出两个Smarr公式，一个是从时间平移不变性，和第二个仅在紧维的精确平移对称的情况下举行。最后，我们表明，'张力第一定律'由Traschen和福克斯在静态的情况下得出的热力学Gibbs-Duhem关系的形式，并给出其在固定的，非旋转的情况下的扩展。

英文摘要：

We study the thermodynamics of Kaluza-Klein black holes with momentum along the compact dimension, but vanishing angular momentum. These black holes are stationary, but non-rotating. We derive the first law for these spacetimes and find that the parameter conjugate to variations in the length of the compact direction is an effective tension, which generally differs from the ADM tension. For the boosted black string, this effective tension is always positive, while the ADM tension is negative for large boost parameter. We also derive two Smarr formulas, one that follows from time translation invariance, and a second one that holds only in the case of exact translation symmetry in the compact dimension. Finally, we show that the `tension first law' derived by Traschen and Fox in the static case has the form of a thermodynamic Gibbs-Duhem relation and give its extension in the stationary, non-rotating case.

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