Non-relativistic metrics with extremal limits

TL;DR

This paper constructs extremal non-relativistic supergravity solutions with Schrödinger asymptotics, analyzes their thermodynamics, and explores phase transitions, revealing that the shear viscosity to entropy density ratio remains universal even at extremality.

Contribution

It introduces new extremal solutions with Schrödinger symmetry derived via TsT transformations and studies their thermodynamic and phase transition properties.

Findings

Shear viscosity to entropy density ratio remains 1/4π at extremality.

Existence of a zero-temperature confinement-deconfinement phase transition.

Solutions include a charged black hole and a soliton with phase transition behavior.

Abstract

We present solutions of type IIB supergravity with z=2 Schrodinger 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 \times 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 1/4\pi even in the extremal limit. We also consider the TsT-transformed 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.