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

Abstract

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

Higher-derivative scalar-vector-tensor theories: black holes, Galileons, singularity cloaking and holography

“…The gauge field is dual to a conserved global current in the QFT, while the scalar drives the low energy dynamics and is dual to the most important scalar operator of the theory, [58,[61][62][63][64][65]. An important ingredient in the analysis of Einstein Maxwell Dilaton theories is the analytical study of asymptotics of physical observables, by a convenient parametrization of the two-derivative effective action, motivated by string-related supergravities, [58]:…”

“…The fact that it has finite entropy at extremality argues against this. This issue can be resolved in the generic Einstein Maxwell Dilaton setup, [58,[61][62][63][64][65]. Then, the low energy fixed point displays hyperscaling violation, [54,66,67].…”

Holography of charged dilaton black holes in general dimensions

“…The corresponding finite-temperature solution can be easily generalized, 12) with the other fields and parameters remaining invariant.…”

“…we can take the following coordinate transformation: 12) to convert the black hole metric into the form of (5.5) with…”

“…The authors also examined the thermodynamics of near extremal black holes and computed the AC conductivity in a zero-temperature background. For related work on charged dilaton black holes see [10,11,12,13].…”