Four-function generalization and separable structures of the Plebanski spacetime with sources

TL;DR

This paper introduces a four-function generalization of the Plebanski spacetime, analyzes its separability properties for particle and wave equations, and discusses potential sources for these generalized metrics.

Contribution

It presents a new four-function family of Plebanski spacetimes, explores their separability features, and proposes possible stress-energy sources.

Findings

Separable Hamilton-Jacobi equations for charged particles

Klein-Gordon equation remains separable in the generalized spacetime

Conditions identified for conformal factors to preserve separability

Abstract

We determine a four-function generalization of the Plebanski spacetime, depending on three arbitrary functions of the radial coordinate, and one function on the angular coordinate. For the generalized Plebanski spacetime, we analyze the separability of the Hamilton--Jacobi equations, and the trajectories of charged test particles are derived from the motion constants. The Klein-Gordon equation separability is established and the Killing horizons are presented as well. Then we introduce a conformal factor to the Plebanski metric and discuss the conditions that preserve the separability. Finally we show a possible stress--energy tensor that may be the source of some of the generalized metrics.