The Thermodynamics of Kaluza-Klein Black Hole/Bubble Chains

Abstract

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 under double analytic continuation of the time and Kaluza-Klein directions. The thermodynamics of bubbles involve a geometrical quantity that we call the bubble surface gravity, which we show has several properties in common with the black hole surface gravity.

20 pages, 1 figure

References in corpus (3)

• Stresses and Strains in the First Law for Kaluza-Klein Black Holes
• The First Law for Boosted Kaluza-Klein Black Holes
• A Microscopic Model for the Black hole - Black string Phase Transition

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