Non-relativistic metrics with extremal limits

Abstract

We present solutions of type IIB supergravity with z = 2 Schrödinger asymptotics that admit an extremal limit, i .e. the black hole horizon has a double zero. These solutions are obtained as TsT transformations of the charged planar black hole in AdS 5 ×S 5 . Unlike the uncharged solution, the Ramond-Ramond two-form is turned on. We study the thermodynamic properties of these new solutions, and we show that the ratio of shear viscosity to entropy density is 1/4π even in the extremal limit. We also consider the TsTtransformed soliton and show that, for a special radius of the compact circle, there is a confinement-deconfinement phase transition at zero temperature between the soliton and black hole phases.

Schrödinger Fermi liquids

“…The U(1) charge chemical potential μ Q and other relevant terms from the current J μ (such as charge density ρ Q and mass density ρ M ) in NRCFT is mapped to the U(1) gauge field A μ of the bulk gravity. Background density β is introduced by the Schrödinger black hole through Null Melvin Twist (or TsT transformation) [22][23][24][25][26]. The physical way to interpret this β could be the density of doping background, or an analog of interaction strength t=U of the Hubbard model.…”

“…We take the AdS 2 rescaling as in [26], send τ → τ=λ and ϵ → λϵ with λ → 0. In this case, the Dirac equation near the AdS 2 boundary becomes ϵ…”

“…Its gravity dual theory had been proposed, with solutions of zero temperature pure Schrödinger (Schr) geometry [20,21], finite temperature black holes [22][23][24], and charged black holes [25,26]. There has been some pursuits on studying fermions in this asymptotic Schrödinger geometry [27][28][29].…”

Shear modes, criticality and extremal black holes

“…It is in this sense that applying the tools of the correspondence to study strongly-interacting condensed matter systems seems to be promising. Recent examples of such applications include modeling superconductivity and superfluidity [2,3,4,5,6], engineering systems with Schrödinger and Lifshitz symmetries [7,8,9,10,11,12,13,14], or modeling a system which can exhibit non-Fermi liquid type behavior [15,16,17,18,19]. See [20,21,22] for reviews.…”

Stability of asymptotically Schrödinger RN black hole and superconductivity

“…This procedure was applied to AdS 5 -Schwarzschild black holes that arise from non-extremal D3 brane backgrounds in [3,4,5]. More recently, Reissner-Nordström (RN) and Kerr-Newman black holes in asymptotically Schrödinger spacetimes were generated [11,12] by applying the Null Melvin Twist to RNAdS 5 black holes arising from non-extremal backgrounds of rotating D3 branes [13,14].…”