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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.
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https://hal.archives-ouvertes.fr/hal-02934062
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Submitted on : Tuesday, September 8, 2020 - 11:11:00 PM
Last modification on : Friday, April 1, 2022 - 3:56:36 AM

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M. Elbistan, P.M. Zhang, G.W. Gibbons, P.A. Horvathy. Lukash plane waves, revisited. JCAP, 2021, 01, pp.052. ⟨10.1088/1475-7516/2021/01/052⟩. ⟨hal-02934062⟩

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