Lukash plane waves, revisited

Abstract

The Lukash metric is a homogeneous gravitational wave which at late times approximates the behaviour of a generic class of spatially homogenous cosmological models with monotonically decreasing energy density. The transcription from Brinkmann to Baldwin-Jeffery-Rosen (BJR) to Bianchi coordinates is presented and the relation to a Sturm-Liouville equation is explained. The 6-parameter isometry group is derived. In the Bianchi VII range of parameters we have two BJR transciptions. However using either of them induces a mere relabeling of the geodesics and isometries. Following pioneering work of Siklos, we provide a self-contained account of the geometry and global structure of the spacetime. The latter contains a Killing horizon to the future of which the spacetime resembles an anisotropic version of the Milne cosmology and to the past of which it resemble the Rindler wedge.

affiliation corrected

Cited by in corpus (9)

• Particle motion in circularly polarized vacuum pp waves
• Gravitational Waves and Conformal Time Transformations
• Memory Effect and Carroll Symmetry: 50 years later
• Gravitational Waves of Type III Shapovalov Spacetimes: Particle Trajectories, Geodesic Deviation and Tidal Accelerations
• Hidden symmetries from distortions of the conformal structure
• Displacement Memory Effect from Supersymmetry
• Conformally related vacuum gravitational waves, and their symmetries
• Gravitational wave of the Bianchi VII universe: particle trajectories, geodesic deviation and tidal accelerations
• Linear perturbations of an exact gravitational wave in the Bianchi IV universe