Penrose Limit and Non-relativistic geometries
For the AdS/CFT duality, considerations of plane wave metric which is obtained as Penrose limit of $AdS_5 \times S^5$ proved to be quite useful and interesting. In this work, we obtain Penrose limit metrics for Lifshitz, Schrodinger, hyperscaling violating Lifshitz and hyperscaling violating Schrodinger geometries. These geometries usually contain singularities for certain range of parameters and we discuss how these singularities appear in the Penrose limit metric. For some cases, there are non-singular metrics possible for certain parameter values and the metric can be extended beyond the coordinate singularity, as discussed in many previous works. Corresponding Penrose limit metrics also display similar features. For the hyperscaling violating Schrodinger metric, we obtain metric extension for some cases.