Phase transitions between Reissner-Nordstrom and dilatonic black holes in 4D AdS spacetime

TL;DR

The authors show that in 4D AdS spacetime, Einstein-Maxwell-dilaton gravity with a non-minimal scalar–gauge coupling renders the AdS-RN black hole unstable below a critical temperature, replacing it with a thermodynamically favored hairy dilatonic black hole. The extremal limit exhibits Lifshitz-like near-horizon geometry, and the dual field theory undergoes a second-order phase transition to a neutral condensate with rich transport behavior, including a Drude-like low-frequency peak and a non-monotonic resistivity akin to Kondo physics. The work combines linear stability analysis, nonlinear numerical construction of hairy solutions, and holographic transport calculations to illuminate the gravity/condensed-matter correspondence and to suggest avenues for embedding in broader supergravity contexts.

Abstract

We study Einstein-Maxwell-dilaton gravity models in four-dimensional anti-de Sitter (AdS) spacetime which admit the Reissner-Nordstrom (RN) black hole solution. We show that below a critical temperature the AdS-RN solution becomes unstable against scalar perturbations and the gravitational system undergoes a phase transition. We show using numerical calculations that the new phase is a charged dilatonic black hole. Using the AdS/CFT correspondence we discuss the phase transition in the dual field theory both for non-vanishing temperatures and in the extremal limit. The extremal solution has a Lifshitz scaling symmetry. We discuss the optical conductivity in the new dual phase and find interesting behavior at low frequencies where it shows a "Drude peak". The resistivity varies with temperature in a non-monotonic way and displays a minimum at low temperatures which is reminiscent of the celebrated Kondo effect.

Figures (15)

• Figure 1: The instability temperature $T_i$ and the black hole temperature $T_{RN}$ as functions of $Q$ for $L=M=1$. Plots extend from $Q=0$ to $Q_\text{ext}=M\sqrt{3}(2L/M)^{1/3}$ which corresponds to extremal black holes. The region of instability is $T_{RN} \ll T_i$. Curves are ordered in a counterclockwise sense for decreasing values of $\gamma$. The smaller $\gamma$ the larger the instability region.
• Figure 2: Some examples of marginally stable modes with $m^2 \ge 0$
• Figure 3: Some examples of marginally stable modes with $0 \ge m^2\geq m_{BF}^2$
• Figure 4: Examples of the field profiles of the numerical charged black hole solution for a coupling function $f(\phi)= \cosh(2\phi)$ and a potential $L^2 V(\phi) = - 6 - \phi^2$. Left panel: the scalar field $\phi$ (black) and the gauge potential $A_0$ (dashed red). Right panel: metric function $g$ (black) and $e^{\chi}$ (dashed red). $T/T_c \sim 0.2$.
• Figure 5: Left panel: Free energy of the hairy black hole (red line) and of the AdS-RN (black dashed line). Right panel: specific heat. The data shown are for the operator ${\cal O}_-$ and for $f(\phi)=\cosh(2\phi)$ and $V(\phi)=-6/L^2-\phi^2/L^2$.