Pleba\'nski-Demia\'nski solutions in bigravity and Kerr-Schild double copy relations using an effective metric

TL;DR

This paper develops a formalism for bigravity solutions using Kerr-Schild ansatz, explores classical double copy relations, and presents new solutions including Plebański-Demiański types with matter coupling and effective metrics.

Contribution

It introduces a proportional generalized double Kerr-Schild ansatz in bigravity with matter coupling and analyzes classical double copy relations for time-dependent and stationary solutions.

Findings

Derived classical Kerr-Schild solutions in bigravity.

Extended double copy relations to time-dependent and stationary cases.

Presented Plebański-Demiański solutions with multiple parameters in bigravity.

Abstract

In this work a formalism for proportional generalized double Kerr-Schild ansatz in bigravity is considered, where both metrics are coupled to matter. We study time-dependent and stationary solutions in the framework of the Kerr-Schild classical double copy and obtain the classical Kerr-Schild for the double, single and zeroth copy equations. For the time-dependent case, we use AdS waves solutions in bigravity previously studied in the literature. For the stationary case, we discuss a kind of Pleba\'nski-Demia\'nski solutions in bigravity which permit different masses, NUT parameters, electric and magnetic charges, while the kinematical parameters are the same, and the cosmological constants related. These solution is presented in Pleba\'nski coordinates, and it is noticed that in these coordinates the description simplifies the classical double copy equations allowing a clearer interpretation in terms of the defined fields. We present and interpret some cases for these solutions for the separate matter sector and using the effective metric.