Spin coefficients for fourdimensional 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. Fourdimensional Walker geometry is exploited to provide examples and the generalization of the real neutral version of Plebański's second heavenly equation to certain Walker geometries given in [P.R. Law, Y. Matsushita, A Spinor approach to Walker geometry, Comm. Math. Phys. 282 (2008) 577623] is extended further.
 Publication:

Journal of Geometry and Physics
 Pub Date:
 August 2009
 DOI:
 10.1016/j.geomphys.2009.04.008
 arXiv:
 arXiv:0802.1761
 Bibcode:
 2009JGP....59.1087L
 Keywords:

 Mathematics  Differential Geometry;
 Mathematical Physics;
 53B30;
 53C50
 EPrint:
 50 pages