Lukash plane waves, revisited
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2020
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| _version_ | 1866913835380637696 |
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| author | Elbistan, M. Zhang, P. M. Gibbons, G. W. Horvathy, P. A. |
| author_facet | Elbistan, M. Zhang, P. M. Gibbons, G. W. Horvathy, P. A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_07801 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Lukash plane waves, revisited Elbistan, M. Zhang, P. M. Gibbons, G. W. Horvathy, P. A. General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory Mathematical Physics 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. |
| title | Lukash plane waves, revisited |
| topic | General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2008.07801 |