Stringy Stability of Charged Dilaton Black Holes with Flat Event Horizon

TL;DR

This paper investigates the stability of charged dilaton black holes with flat horizons in anti-de Sitter space, revealing how dilaton coupling affects their vulnerability to brane pair-production instability, with implications for AdS/CFT applications.

Contribution

It provides a detailed analysis of the stability conditions of Gao-Zhang charged dilaton black holes, highlighting the role of the dilaton coupling parameter in their stability against brane pair-production.

Findings

For α > 1, black holes are stable against brane pair production.

For 0 < α < 1, increasing charge leads to instability.

Seiberg-Witten action diverges logarithmically at infinity for finite α.

Abstract

Electrically charged black holes with flat event horizon in anti-de Sitter space have received much attention due to various applications in Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, from modeling the behavior of quark-gluon plasma to superconductor. Crucial to the physics on the dual field theory is the fact that when embedded in string theory, black holes in the bulk may become vulnerable to instability caused by brane pair-production. Since dilaton arises naturally in the context of string theory, we study the effect of coupling dilaton to Maxwell field on the stability of flat charged AdS black holes. In particular, we study the stability of Gao-Zhang black holes, which are locally asymptotically anti-de Sitter. We find that for dilaton coupling parameter $\alpha$ > 1, flat black holes are stable against brane pair production, however for 0 < $\alpha$ < 1, the black holes eventually become unstable as the amount of electrical charges is increased. Such instability however, behaves somewhat differently from that of flat Reissner-Nordstr\"om black holes. In addition, we prove that the Seiberg-Witten action of charged dilaton AdS black hole of Gao-Zhang type with flat event horizon (at least in 5-dimension) is always logarithmically divergent at infinity for finite values of $\alpha$, and is finite and positive in the case $\alpha$ tends to infinity . We also comment on the robustness of our result for other charged dilaton black holes that are not of Gao-Zhang type.