Interpretation of the Siklos solutions as exact gravitational waves in the anti-de Sitter universe

TL;DR

This paper analyzes Siklos solutions of Einstein's equations, revealing they describe exact gravitational waves in anti-de Sitter space, with implications for understanding wave propagation in curved, non-flat backgrounds.

Contribution

It provides an analytical interpretation of Siklos solutions as gravitational waves in anti-de Sitter space, including detailed analysis of the Kaigorodov spacetime as a cosmological analogue.

Findings

Siklos solutions represent gravitational waves in anti-de Sitter universe.

The background space is non-asymptotically flat due to negative cosmological constant.

Kaigorodov spacetime serves as a cosmological analogue of flat pp-waves.

Abstract

The Siklos class of solutions of Einstein's field equations is investigated by analytical methods. By studying the behaviour of free particles we reach the conclusion that the space-times represent exact gravitational waves propagating in the anti-de Sitter universe. The presence of a negative cosmological constant implies that the 'background' space is not asymptotically flat and requires a 'rotating' reference frames in order to fully simplify and view the behaviour of nearby test particles. The Kaigorodov space-time, which is the simplest representative of the Siklos class, is analyzed in more detail. It is argued that it may serve as a 'cosmological' analogue of the well-known homogeneous pp-waves in the flat universe.