Phase structure of black branes in grand canonical ensemble

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.

arXiv comment32 pages, 2 figures, various points refined, discussion expanded, references updated, typos corrected, published in JHEP 1105:091,2011

References in corpus (15)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Large N Field Theories, String Theory and Gravity
• String Solitons
• The Gravitational Hamiltonian, Action, Entropy, and Surface Terms
• Black and super p-branes in diverse dimensions
• The Black Branes of M-theory
• The Non-BPS Black Hole Attractor Equation
• An instability of higher-dimensional rotating black holes
• Extremal limits and black hole entropy
• Phase Transitions and Critical Behavior for Charged Black Holes
• Thermodynamics of toroidal black holes
• On Attractor Mechanism and Entropy Function for Non-extremal Black Holes/Branes
• Thermodynamic instability of doubly spinning black objects
• Thermodynamics of a black hole in a cavity

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• The enriched phase structure of black branes in canonical ensemble