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

Abstract We determine a four-function generalization of the Plebański spacetime, depending on three arbitrary functions of the radial coordinate and one function on the angular coordinate. For the generalized Plebański spacetime, we analyze the separability of the Hamilton–Jacobi equations, and the trajectories of a charged test particle 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 Plebański 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.