Metastability of R-Charged Black Holes

TL;DR

This paper investigates the stability of R-charged AdS black holes in a grand canonical ensemble, identifying a critical chemical potential for metastability and relating it to dual field theory predictions.

Contribution

It introduces a reduced action approach to analyze metastability without solving equations of motion, and proposes a boundary temperature consistent with AdS/CFT.

Findings

Metastability occurs at a critical chemical potential.

The relation between small and large black holes and instability is clarified.

A more general solution of the theory is found and discussed.

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.