# The first law for boosted Kaluza-Klein black holes

@article{Kastor2007TheFL, title={The first law for boosted Kaluza-Klein black holes}, author={David Kastor and Sourya Ray and Jennie Traschen}, journal={Journal of High Energy Physics}, year={2007}, volume={2007}, pages={026-026} }

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…

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## 25 References

### Stresses and strains in the first law for Kaluza-Klein black holes

- Physics
- 2006

We consider how variations in the moduli of the compactification manifold contribute `pdV' type work terms to the first law for Kaluza-Klein black holes. We give a new proof for the S1 case, based on…

### Tension perturbations of black brane spacetimes

- Physics
- 2004

We consider black brane spacetimes that have at least one spatial translation Killing field that is tangent to the brane. A new parameter, the tension of a spacetime, is defined. The tension…

### A Higher Dimensional Stationary Rotating Black Hole Must be Axisymmetric

- Mathematics
- 2006

A key result in the proof of black hole uniqueness in 4-dimensions is that a stationary black hole that is “rotating”—i.e., is such that the stationary Killing field is not everywhere normal to the…

### Extrema of mass, stationarity, and staticity, and solutions to the Einstein-Yang-Mills equations.

- MathematicsPhysical review. D, Particles and fields
- 1992

A generalization of the argument to the case in which an interior boundary is present proves that a necessary condition for a solution of the Einstein-Yang-Mills equation to be an extremum of mass at fixed area of the boundary surface is that the solution be static.

### Instabilities of black strings and branes

- Physics
- 2007

We review recent progress on the instabilities of black strings and branes both for pure Einstein gravity as well as supergravity theories which are relevant for string theory. We focus mainly on…

### BLACK STRING AND VELOCITY FRAME DRAGGING

- Physics
- 2008

We investigate velocity frame dragging with the boosted Schwarzschild black string solution and the boosted Kaluza–Klein bubble solution, in which a translational symmetry along the boosted…

### The first law of black brane mechanics

- Physics
- 2001

We obtain ADM and Komar surface integrals for the energy density, tension and angular momentum density of stationary p-brane solutions of Einstein's equations. We use them to derive a Smarr-type…

### The four laws of black hole mechanics

- Physics
- 1973

Expressions are derived for the mass of a stationary axisymmetric solution of the Einstein equations containing a black hole surrounded by matter and for the difference in mass between two…