Hidden horizons in non - relativistic AdS / CFT

We study boundary Green’s functions for spacetimes with non-relativistic scaling symmetry. For this class of backgrounds, scalar modes with large transverse momentum, or equivalently low frequency, have an exponentially suppressed imprint on the boundary. We investigate the effect of these modes on holographic two-point functions. We find that the boundary Green’s function is generically insensitive to horizon features on small transverse length scales. We explicitly demonstrate this insensitivity for Lifshitz z = 2, and then use the WKB approximation to generalize our findings to Lifshitz z > 1 and RG flows with a Lifshitz-like region. We also comment on the analogous situation in Schrödinger spacetimes. Finally, we exhibit the analytic properties of the Green’s function in these spacetimes.