Asymptotically Schrödinger space-times

Abstract

We first review how asymptotically Schrödinger space-times arise in a natural way by performing a TsT transformation on asymptotically AdS space-times and some of its consequences. We then give a coordinate independent definition of a pure Schrödinger space-time in terms of an AdS metric and an AdS null Killing vector. Furthermore, by analogy with the AdS case, we provide a local coordinate independent definition of a Schrödinger boundary in terms of a defining function. Finally this directly leads us to the construction of a Fefferman-Graham expansion for locally Schrödinger space-times.