Homogeneous spacetimes and separation of variables in the Hamilton–Jacobi equation

Abstract

We discuss a classification of spatially homogeneous nonisotropic spacetimes, which admit a separation of variables in the Hamilton–Jacobi equation. Spacetimes with a four-parametric group of motion are considered. All types of metrics and Killing vectors of these spacetimes with Bianchi classification are obtained. An example of application for the Vaidya problem is considered.