Phase structure of black branes in grand canonical ensemble

TL;DR

This paper investigates the phase structure and thermodynamics of charged black p-branes in a grand canonical ensemble, revealing new stability conditions and phase transitions, including an analog of the Hawking-Page transition.

Contribution

It extends previous canonical ensemble analysis to the grand canonical ensemble, uncovering differences in stability and phase structure for black p-branes.

Findings

Existence of an analog of Hawking-Page transition for charged black p-branes.

Stable brane phase disappears above a certain temperature in grand canonical ensemble.

Phase structure similar to zero-charge case under specific potential conditions.

Abstract

This is a companion paper of our previous work [1] where we studied the thermodynamics and phase structure of asymptotically flat black $p$-branes in a cavity in arbitrary dimensions $D$ in a canonical ensemble. In this work we study the thermodynamics and phase structure of the same in a grand canonical ensemble. Since the boundary data in two cases are different (for the grand canonical ensemble boundary potential is fixed instead of the charge as in canonical ensemble) the stability analysis and the phase structure in the two cases are quite different. In particular, we find that there exists an analog of one-variable analysis as in canonical ensemble, which gives the same stability condition as the rather complicated known (but generalized from black holes to the present case) two-variable analysis. When certain condition for the fixed potential is satisfied, the phase structure of charged black $p$-branes is in some sense similar to that of the zero charge black $p$-branes in canonical ensemble up to a certain temperature. The new feature in the present case is that above this temperature, unlike the zero-charge case, the stable brane phase no longer exists and `hot flat space' is the stable phase here. In the grand canonical ensemble there is an analog of Hawking-Page transition, even for the charged black $p$-brane, as opposed to the canonical ensemble. Our study applies to non-dilatonic as well as dilatonic black $p$-branes in $D$ space-time dimensions.