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arXiv · 2409.08344

Newman-Penrose formalism and exact vacuum solutions to conformal Weyl gravity

Petr Jizba·Kamil Mudruňka
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Abstract

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--Nordstr\"{o}m-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.

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Petr Jizba, Kamil Mudruňka. 2024-09-12. Newman-Penrose formalism and exact vacuum solutions to conformal Weyl gravity. https://doi.org/10.1103/physrevd.110.124006

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