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arXiv · 2008.07801

Lukash plane waves, revisited

M. Elbistan·P. M. Zhang·G. W. Gibbons·P. A. Horvathy
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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.

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M. Elbistan, P. M. Zhang, G. W. Gibbons, P. A. Horvathy. 2020-08-18. Lukash plane waves, revisited. https://doi.org/10.1088/1475-7516/2021/01/052

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