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

TL;DR

This paper investigates phase transitions between Reissner-Nordstrom and dilatonic black holes in 4D AdS spacetime, revealing a new charged dilatonic phase with unique optical and resistive properties linked to dual field theories.

Contribution

It demonstrates the instability of AdS-RN black holes below a critical temperature and characterizes the resulting charged dilatonic black hole phase using numerical methods.

Findings

AdS-RN black holes become unstable below a critical temperature.

The new phase exhibits Lifshitz scaling symmetry.

Optical conductivity shows a Drude peak and non-monotonic resistivity.

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.