The conformal Penrose limit: back to square one

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 MD = Md × B, where Md 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 MD through the conformal Killing potential of Md and prove that Md has a conformal Penrose limit if and only if MD has an ordinary plane wave limit. Further properties of the limit are discussed.