Schrödinger geometries arising from Yang-Baxter deformations

We present further examples of the correspondence between deformed AdS 5 ×S 5 solutions of type IIB supergravity and classical r -matrices satisfying the classical YangBaxter equation (CYBE). In the previous works, classical r -matrices have been composed of generators of only one of either so(2 , 4) or so(6) . In this paper, we consider some examples of r -matrices with both of them. The r -matrices of this kind contain (generalized) Schrödinger spacetimes and gravity duals of dipole theories. It is known that the generalized Schrödinger spacetimes can also be obtained via a certain class of TsT transformations called null Melvin twists. The metric and NS-NS two-form are reproduced by following the Yang-Baxter sigma-model description