Penrose Limit and Non-relativistic geometries

TL;DR

This paper explores Penrose limits of various non-relativistic geometries relevant to holography, analyzing singularities and extensions of the resulting plane wave metrics for Lifshitz, Schrödinger, and hyperscaling violating spacetimes.

Contribution

It derives Penrose limit metrics for several non-relativistic geometries and discusses their singularity structures and possible extensions, extending previous analyses beyond AdS spaces.

Findings

Penrose limits of Lifshitz and Schrödinger geometries obtained.

Singularities in the original geometries manifest in the Penrose limit.

Some metrics can be extended beyond coordinate singularities.

Abstract

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.