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.

arXiv comment18 pages, revtex4

References in corpus (19)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies
• Cosmological parameters from SDSS and WMAP
• Fitting galactic rotation curves with conformal gravity and a global quadratic potential
• Impact of a global quadratic potential on galactic rotation curves
• Classical tests for Weyl gravity: deflection of light and time delay
• Fitting dwarf galaxy rotation curves with conformal gravity
• Conformal Weyl gravity and perihelion precession
• Gauge choice and geodetic deflection in conformal gravity
• Universal Properties of Galactic Rotation Curves and a First Principles Derivation of the Tully-Fisher Relation
• Inflationary cosmology from quantum Conformal Gravity
• Weyl gravity and Cartan geometry
• Reissner-Nordstrøm-de Sitter Manifold : Photon Sphere and Maximal Analytic Extension
• Causal Structure of Vacuum Solutions to Conformal(Weyl) Gravity
• Infrared behavior of Weyl Gravity: Functional Renormalization Group approach
• The Newman-Penrose formalism in quadratic gravity

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