Black holes and non-relativistic quantum systems

TL;DR

This paper explores black hole solutions in higher dimensions that correspond to non-relativistic quantum systems with scale invariance, revealing thermodynamic and transport properties similar to those of a free Fermi gas.

Contribution

It introduces a gravitational model with specific fields that holographically describe non-relativistic quantum systems with dynamical exponent z=2.

Findings

Energy per particle matches that of a non-interacting Fermi gas

Shear viscosity to entropy density ratio is $rac{ mp}{4 extpi}$

Provides a gravitational dual for non-relativistic quantum systems

Abstract

We describe black holes in d+3 dimensions, whose thermodynamic properties correspond to those of a scale invariant non-relativistic d+1 dimensional quantum system with dynamical exponent z=2. The gravitational model involves a massive abelian vector field and a scalar field, in addition to the metric. The energy per particle in the dual theory is $|\mu| d/(d+2)$, exactly as in a non-interacting Fermi gas, while the ratio of shear viscosity to entropy density is $\hbar/4\pi$.