The Conformal Penrose Limit: Back to Square One

TL;DR

This paper demonstrates that the conformal Penrose limit can be understood as a standard plane wave limit within a higher-dimensional Ricci-flat spacetime framework, providing insights into resolving spacetime singularities.

Contribution

It establishes a link between conformal Penrose limits and ordinary plane wave limits in higher dimensions using Ricci-flat manifolds with specific geometric structures.

Findings

Conformal Penrose limit corresponds to an ordinary plane wave limit in higher dimensions.

The higher-dimensional Ricci-flat manifold is constructed from Einstein and Sasaki-Einstein spaces.

Properties of the limits and their implications for spacetime singularities are discussed.

Abstract

We show that the conformal Penrose limit is an ordinary plane wave limit in a higher dimensional framework which resolves the spacetime singularity. The higher dimensional framework is provided by Ricci-flat manifolds which are of the form M_D = M_d x B, where M_d is an Einstein spacetime that has a negative cosmological constant and admits a spacelike conformal Killing vector, and B is a complete Sasaki-Einstein space with constant sectional curvature. We define the Kaluza-Klein metric of M_D through the conformal Killing potential of M_d and prove that M_d has a conformal Penrose limit if and only if M_D has an ordinary plane wave limit. Further properties of the limit are discussed.