Asymptotically Schroedinger Space-Times: TsT Transformations and Thermodynamics

TL;DR

This paper investigates a class of 5D asymptotically Schroedinger space-times derived via TsT transformations from AdS spaces, analyzing their boundaries, on-shell action, and thermodynamics, including phase transitions.

Contribution

It characterizes the complete class of such space-times, demonstrates TsT invariance of the on-shell action and black hole thermodynamics, and explores phase transitions in Schroedinger backgrounds.

Findings

TsT transformations preserve the on-shell action.

Black hole thermodynamics remains TsT invariant.

A Hawking-Page type phase transition occurs in thermal Schroedinger space-times.

Abstract

We study the complete class of 5-dimensional asymptotically Schroedinger space-times that can be obtained as the TsT transform of a 5-dimensional asymptotically AdS space-time. Based on this we identify a conformal class of Schroedinger boundaries. We use a Fefferman-Graham type expansion to study the on-shell action for this class of asymptotically Schroedinger space-times and we show that its value is TsT invariant. In the second part we focus on black hole space-times and prove that black hole thermodynamics is also TsT invariant. We use this knowledge to argue that thermal global Schroedinger space-time at finite chemical potential undergoes a Hawking-Page type phase transition.