Lukash plane waves, revisited
  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.
