Weyl double copy in type D spacetime in four and five dimensions

TL;DR

This paper extends the Weyl double copy framework to four and five-dimensional type D spacetimes, showing how vacuum solutions relate to Maxwell scalars and scalar fields satisfying the Klein-Gordon equation.

Contribution

It provides a new realization of the Weyl double copy in four dimensions and extends this relation to five-dimensional type D spacetimes.

Findings

Any four-dimensional type D vacuum solution admits a Maxwell scalar that squares to the Weyl scalar.

The scalar field in the double copy satisfies the Klein-Gordon equation with a source.

The framework is successfully extended to five-dimensional type D spacetimes.

Abstract

In this paper, we present a second realization of the Weyl double copy (WDC) in four-dimensional algebraic type D spacetime. We show that any type D vacuum solution admits an algebraically general Maxwell scalar on the curved background that squares to give the Weyl scalar. The WDC relation defines a scalar field that satisfies the Klein-Gordon equation sourced by the Weyl scalar on the curved background. We then extend the type D WDC to five dimensions.