The First Law for Boosted Kaluza-Klein Black Holes

Details The First Law for Boosted Kaluza-Klein Black Holes The First Law for Boosted Kaluza-Klein Black Holes

2007-04-05

arxiv.org/abs/0704.0729v2

JHEP 0706:026,2007

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, 0 figures; v2 - reference added

Scientific paper

10.1088/1126-6708/2007/06/026

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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