Bubbles and black branes in the grand canonical ensemble

Abstract

When the phase structure of the black brane in a grand canonical ensemble is discussed, the bubble phase with the same boundary data should be included in this structure. As such, the phase transitions among bubbles, black branes, and ``hot flat space'' are possible, therefore giving a much enriched phase structure. We also argue that under some conditions, either the grand canonical ensemble itself is unstable or there are some unknown new phases.