Shapovalov wave-like spacetimes

TL;DR

This paper classifies wave-like Shapovalov spacetimes allowing complete separation of variables in the Hamilton-Jacobi equation, and provides exact Einstein solutions with a cosmological constant for these models.

Contribution

It introduces a complete classification of wave-like Shapovalov spacetimes and derives exact Einstein solutions with a cosmological constant for these models.

Findings

Classification of wave-like Shapovalov spaces achieved.

Exact vacuum Einstein solutions with cosmological constant found.

Complete integrals for eikonal and Hamilton-Jacobi equations provided.

Abstract

A complete classification of space-time models is presented, which admit the privileged coordinate systems, where the Hamilton-Jacobi equation for a test particle is integrated by the method of complete separation of variables with separation of the isotropic (wave) variable, on which the metric of space depends (wave-like Shapovalov spaces). For all types of Shapovalov spaces, exact solutions of the Einstein equations with a cosmological constant in vacuum are found. Complete integrals are presented for the eikonal equation and the Hamilton-Jacobi equation of motion of test particles.