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

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

2008-02-13

arxiv.org/abs/0802.1761v2

Journal of Geometry and Physics, 59(8), 1087-1126, 2009

Mathematics

Differential Geometry

50 pages; minor typos corrected in v2

Scientific paper

10.1016/j.geomphys.2009.04.008

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 Pleba\~nski's (1975) second heavenly equation to certain Walker geometries given in Law and Matsushita [16] is extended further.

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