Spin coefficients for four-dimensional neutral metrics, and null geometry

Abstract

Notation for spin coefficients for metrics of neutral signature in four dimensions is introduced. The utility and interpretation of spin coefficients is explored through themes in null geometry familiar from (complex) general relativity. Four-dimensional Walker geometry is exploited to provide examples and the generalization of the real neutral version of Plebañski's (1975) second heavenly equation to certain Walker geometries given in Law and Matsushita [16] is extended further.

50 pages; minor typos corrected in v2

References in corpus (4)

• Anti-self-dual four-manifolds with a parallel real spinor
• A spinor approach to Walker geometry
• Walker's theorem without coordinates
• Algebraically Special, Real Alpha Geometries

Cited by in corpus (8)

• Pseudo-Riemannian VSI spaces II
• Real AlphaBeta-Geometries
• Pseudo-Riemannian VSI spaces
• Algebraically Special, Real Alpha Geometries
• Algebraic Classification of the Ricci Curvature Tensor and Spinor for Neutral Signature in Four Dimensions
• Mathematical Properties of a Class of Four-dimensional Neutral Signature Metrics
• Sharp version of the Goldberg-Sachs theorem
• Universal Walker metrics