Interpretation of twisting type N vacuum solutions with cosmological constant

TL;DR

This paper introduces a new class of twisting type N vacuum solutions with positive cosmological constant, showing they represent gravitational waves in de-Sitter space and exploring their properties like horizons and cosmic no-hair conjecture.

Contribution

It generalizes previous non-twisting solutions to include twisting cases, revealing their interpretation as gravitational waves in de-Sitter universe with wave amplitudes linked to Lambda.

Findings

Twisting type N solutions act as gravitational waves in de-Sitter space.

Wave amplitudes are proportional to the cosmological constant Lambda.

The solutions support the cosmic no-hair conjecture and have identifiable Killing horizons.

Abstract

We investigate a new class of twisting type N vacuum solutions with nonzero (positive) cosmological constant Lambda by studying the equations of geodesic deviations along the privileged radial timelike geodesics, generalizing J. Bicak and J. Podolsky's results on non-twisting type N solutions. It is shown that these twisting radiative spacetimes can be interpreted as exact transverse gravitational waves propagating in the de-Sitter universe, with a distinctive feature that all the wave amplitudes are proportional to Lambda (dark energy/matter source coupling). Moveover, we demonstrate the cosmic no-hair conjecture in these spacetimes and discuss their Killing horizons.