The Thermodynamics of Kaluza-Klein Black Hole/Bubble Chains

TL;DR

This paper explores the thermodynamics of Kaluza-Klein black hole and bubble chains, revealing an interchange symmetry between black hole horizons and KK bubbles, and introducing the concept of bubble surface gravity.

Contribution

It computes bubble contributions to Smarr relations and first laws, highlighting a novel symmetry and defining bubble surface gravity with properties similar to black hole surface gravity.

Findings

Derived new relations involving black holes and KK bubbles.

Identified an interchange symmetry between black hole and bubble properties.

Introduced the concept of bubble surface gravity with black hole-like properties.

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.