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.Comment: References adde
