Newman-Penrose formalism and exact vacuum solutions to conformal Weyl gravity
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915060042956800 |
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| author | Jizba, Petr Mudruňka, Kamil |
| author_facet | Jizba, Petr Mudruňka, Kamil |
| contents | We study the exterior solution for a static, spherically symmetric source in Weyl conformal gravity in terms of the Newman--Penrose formalism. We first show that both the static, uncharged black hole solution of Mannheim and Kazanas and the static, charged Reissner--Nordström-like solution can be found more easily in this formalism than in the traditional coordinate-basis approach, where the metric tensor components are taken as the basic variables. Second, we show that the Newman-Penrose formalism offers a particularly convenient framework that is well suited for the discussion of conformal gravity solutions corresponding to Petrov "type-D" spacetimes. This is illustrated with a two-parameter class of wormhole solutions that includes the Ellis--Bronnikov wormhole solution of Einstein's gravity as a limiting case. Other salient issues, such as the gauge equivalence of solutions and the inclusion of the electromagnetic field are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08344 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Newman-Penrose formalism and exact vacuum solutions to conformal Weyl gravity Jizba, Petr Mudruňka, Kamil General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics We study the exterior solution for a static, spherically symmetric source in Weyl conformal gravity in terms of the Newman--Penrose formalism. We first show that both the static, uncharged black hole solution of Mannheim and Kazanas and the static, charged Reissner--Nordström-like solution can be found more easily in this formalism than in the traditional coordinate-basis approach, where the metric tensor components are taken as the basic variables. Second, we show that the Newman-Penrose formalism offers a particularly convenient framework that is well suited for the discussion of conformal gravity solutions corresponding to Petrov "type-D" spacetimes. This is illustrated with a two-parameter class of wormhole solutions that includes the Ellis--Bronnikov wormhole solution of Einstein's gravity as a limiting case. Other salient issues, such as the gauge equivalence of solutions and the inclusion of the electromagnetic field are also discussed. |
| title | Newman-Penrose formalism and exact vacuum solutions to conformal Weyl gravity |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2409.08344 |