# The thermodynamics of Kaluza–Klein black hole/bubble chains

@article{Kastor2008TheTO, title={The thermodynamics of Kaluza–Klein black hole/bubble chains}, author={David Kastor and Sourya Ray and Jennie Traschen}, journal={Classical and Quantum Gravity}, year={2008}, volume={25}, pages={125004} }

A Killing bubble is a minimal surface that arises as the fixed surface of a spacelike Killing field. We compute the bubble contributions to the Smarr relations and the mass and tension first laws for spacetimes containing both black holes and Killing bubbles. The resulting relations display an interesting interchange symmetry between the properties of black hole horizons and those of KK bubbles. This interchange symmetry reflects the underlying relation between static bubbles and black holes…

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