Metastability of R-Charged Black Holes

Abstract

The global stability of R-charged AdS black holes in a grand canonical ensemble is examined by eliminating the constraints from the action, but without solving the equations of motion, thereby constructing the reduced action of the system. The metastability of the system is found to set in at a critical value of the chemical potential which is conjugate to the R-charge. The relation among the small black hole, large black hole and the instability is discussed. The result is consistent with the metastability found in the AdS/CFT-conjectured dual field theory. The "renormalized" temperature of AdS black holes, which has been rather ad hoc, is suggested to be the boundary temperature in the sense of AdS/CFT correspondence. As a byproduct of the analysis, we find a more general solution of the theory and its properties are briefly discussed.

arXiv comment36 pages, 7 figures, v2 is the published version. the exposition is made slightly shorter and hopefully clearer

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• N=4 SYM on S^3 with Near Critical Chemical Potentials
• Holographic Roberge-Weiss Transitions
• Novel color superconducting phases of $\mathcal{N}$ = 4 super Yang-Mills at strong coupling
• Fragmentation of Spinning Branes
• Holography of the Quark Matter Triple Point
• Shearing Black Holes and Scans of the Quark Matter Phase Diagram
• Weak coupling large-N transitions at finite baryon density
• Brane nucleation instabilities in non-AdS/non-CFT
• Dual Dressed Black Holes as the end point of the Charged Superradiant instability in $\mathcal{N}=4$ Yang Mills
• Polarised Black Holes in ABJM
• A Universal Lower Bound on the Specific Temperatures of AdS-Reissner-Nordstrom Black Holes with Flat Event Horizons
• Black hole phase transitions via Bragg-Williams
• Spinning flavour branes and fermion pairing instabilities
• Phase Structure of Beta-deformed N=4 SYM on S^3 with Chemical Potentials