The Penrose limit of the Weyl double copy

TL;DR

This paper integrates the Penrose limit into the Weyl double copy framework, extending the double copy correspondence from plane wave spacetimes to black hole geometries and clarifying ambiguities in Petrov type N spacetimes.

Contribution

It introduces a novel embedding of the Penrose limit into the Weyl double copy, enabling the extension of double copy properties to more general spacetime backgrounds.

Findings

Provides a lift of double copy properties to black hole geometries.

Fixes functional ambiguity in Petrov type N spacetimes.

Derives an analytical expression for Penrose limits of vacuum type D spacetimes.

Abstract

We embed the Penrose limit into the Weyl classical double copy. Thereby, we provide a lift of the double copy properties of plane wave spacetimes into black hole geometries and we open a novel avenue towards taking the classical double copy beyond statements about algebraically special backgrounds. In particular, the Penrose limit, viewed as the leading order Fermi coordinate expansion around a null geodesic, complements approaches leveraging asymptotic flatness such as the asymptotic Weyl double copy. Along the way, we show how our embedding of the Penrose limit within the Weyl double copy naturally fixes the functional ambiguity in the double copy for Petrov type N spacetimes. We also highlight the utility of a spinorial approach to the Penrose limit. In particular, we use this spinorial approach to derive a simple analytical expression for arbitrary Penrose limits of four-dimensional, vacuum type D spacetimes.