On type-II Spacetimes and the Double Copy for Fluids Metrics

TL;DR

This paper extends the double copy framework to type-II fluid-dual spacetimes, demonstrating a viable double copy construction using perturbative near-horizon expansions and Maxwell spinor ansatz.

Contribution

It introduces a method to construct the double copy for more general fluids in type-II spacetimes, building on previous work on type-D and type-N fluids.

Findings

A viable type-II double copy is demonstrated using stream functions.

Near horizon expansion allows generalization of the double copy.

A Maxwell spinor ansatz with bi-spinor components is essential at lowest order.

Abstract

In our previous paper (arXiv:2005.04242) we discussed type-D and type-N fluid-dual spacetimes and provided their associated single copies in the context of the Weyl double copy. In this work we extend our analysis to more general fluids thereby requiring the application of the double copy picture to type-II space-times. By combining our previous type-D and type-N fluids via their associated stream functions we demonstrate an example of a viable type-II double copy. Further we use an explicitly perturbative approach in the near horizon expansion to generalize the type II double copy for the fluid-dual space-times. We show a Maxwell spinor ansatz containing a heterogeneous bi-spinor component is necessary to provide a viable type-II double copy at the lowest order.