Weyl double copy in Lifshitz spacetimes

TL;DR

This work probes the compatibility of Kerr-Schild and Weyl formulations of the classical double copy in Lifshitz spacetimes. By applying a regularization prescription to Lifshitz black hole solutions, the authors demonstrate that the Weyl double copy can be reconciled with the Kerr-Schild double copy across three new examples, including a two-term regularization scenario, an $R^2$-corrected case, and a stationary Lifshitz black hole. The method consistently handles conformally flat contributions and vanishing Weyl or $Z$ data, restoring the CC between gravity and gauge fields in each instance. The results strengthen the case that regularization is a robust ingredient for the Weyl double copy in nontrivial backgrounds and motivate broader checks in Lifshitz and higher-curvature settings with potential holographic relevance.

Abstract

Lifshitz black hole solutions pose particular challenges for reconciling the two main formulations of the classical double copy: the Kerr-Schild double copy and the Weyl double copy. Recent work has suggested that consistency between the two can be restored, in certain cases, only by adopting a regularization prescription in the Weyl double copy. In this paper, we test this prescription on three examples from the literature, each with a distinct novel feature, and show that the prescription remains valid in all cases.