Minisuperspace Double Copy in Lifshitz Spacetimes

TL;DR

This paper formulates a minisuperspace approach to the classical double copy in Lifshitz spacetimes, revealing a universal structure and extending the framework to higher-curvature theories and black hole solutions.

Contribution

It introduces a novel minisuperspace formulation of the double copy for Lifshitz spacetimes, capturing theory dependence via a single potential and demonstrating universality across different models.

Findings

Identifies a radial operator reproducing the Maxwell operator from gravitational dynamics.

Shows the universal origin of the additional term in non-relativistic Lifshitz backgrounds.

Extends the formalism to higher-curvature theories and verifies in Einstein--Gauss--Bonnet gravity.

Abstract

We develop a minisuperspace formulation of the classical double copy for anisotropic Lifshitz spacetimes in arbitrary dimension. By imposing static symmetries at the level of the action, the gravitational system reduces to an effective one-dimensional radial problem with a universal structure, in which all theory dependence is captured by a single potential. Within this framework, we identify a radial operator that reproduces the Maxwell operator for the temporal component of the single-copy field directly from the reduced gravitational dynamics, without using the equations of motion. For non-relativistic Lifshitz backgrounds, this relation is modified by an additional contribution that encodes the deviation from maximal symmetry. We show that this term has a universal origin, determined by anisotropic scaling and horizon geometry, and that it vanishes smoothly in the relativistic limit. After imposing the Hamiltonian constraint, the matter sector generates the corresponding source term, reproducing known single-copy charge densities when a Kerr--Schild description exists and extending them beyond this setting. We further demonstrate that the same mechanism persists in higher-curvature theories, where the effective potential is replaced by its higher-order generalization while preserving the operator structure. Explicit Lifshitz black hole solutions illustrate how matter content and horizon topology enter the construction. As an additional check, we verify the consistency of the formalism in the relativistic limit using a charged AdS solution in Einstein--Gauss--Bonnet gravity.