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

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.

Note:

19 pages - v2: minor corrections and additional references -v3: Figs.5 changed and additional comments. Version accepted in JHEP

AdS-CFT Correspondence
Black Holes in String Theory
Black Holes
space-time: anti-de Sitter
perturbation: scalar
field theory: conformal
dimension: 4
critical phenomena
black hole: Reissner-Nordstroem
numerical calculations

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