Non-relativistic metrics with extremal limits

TL;DR

The work constructs non-relativistic holographic backgrounds with Schrödinger symmetry ($z=2$) by TsT transforming a charged AdS black hole in type IIB supergravity, producing backgrounds with a nontrivial RR two-form and NS-NS B-field. It analyzes the extremal limit, revealing a double-zero horizon and two distinct near-horizon configurations, and demonstrates that the universal ratio $\eta/s=1/(4\pi)$ persists even at zero temperature. The thermodynamics reveals a grand potential identical in form to the undeformed case and confirms a non-relativistic equation of state $P V = E$, with the entropy matching the Bekenstein–Hawking result. Furthermore, the TsT-transformed soliton exhibits a zero-temperature confinement–deconfinement transition controlled by the chemical potentials $\mu_1$ and $\mu_2$, occurring only for special circle radii, which enriches the phase structure of non-relativistic holographic systems and motivates exploration of decoupled AdS$_2$ sectors and potential Fermi surface physics.

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 1/4πeven 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.