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

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--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.

18 pages, revtex4

References in corpus (5)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Impact of a global quadratic potential on galactic rotation curves
• Conformal Weyl gravity and perihelion precession
• Inflationary cosmology from quantum Conformal Gravity
• The Newman-Penrose formalism in quadratic gravity

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