Sachs equations and plane waves, I: Rosen universes
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913306706444288 |
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| author | Holland, Jonathan Sparling, George |
| author_facet | Holland, Jonathan Sparling, George |
| contents | This article, the first in a series, analyzes the general theory of plane wave spacetimes. Following Dmitri Aleekseevsky, these are defined as spacetimes admitting a group of dilations leaving invariant a smooth curve. If this curve is specified as part of the structure, the spacetime is termed a Penrose limit, whose theory was developed first by Roger Penrose. The main result is that every plane wave is a Rosen universe, a generalization of the smooth metrics of Albert Einstein and Nathan Rosen, allowing for certain isolated co-ordinate singularities; the latter are characterized. We conclude with an extended example, using the techniques developed in the article to associate a vacuum plane wave in four dimensions to any hyperbolic billiard trajectory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07036 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sachs equations and plane waves, I: Rosen universes Holland, Jonathan Sparling, George General Relativity and Quantum Cosmology Mathematical Physics 83C35 This article, the first in a series, analyzes the general theory of plane wave spacetimes. Following Dmitri Aleekseevsky, these are defined as spacetimes admitting a group of dilations leaving invariant a smooth curve. If this curve is specified as part of the structure, the spacetime is termed a Penrose limit, whose theory was developed first by Roger Penrose. The main result is that every plane wave is a Rosen universe, a generalization of the smooth metrics of Albert Einstein and Nathan Rosen, allowing for certain isolated co-ordinate singularities; the latter are characterized. We conclude with an extended example, using the techniques developed in the article to associate a vacuum plane wave in four dimensions to any hyperbolic billiard trajectory. |
| title | Sachs equations and plane waves, I: Rosen universes |
| topic | General Relativity and Quantum Cosmology Mathematical Physics 83C35 |
| url | https://arxiv.org/abs/2402.07036 |