Space-Times Admitting Killing-Yano Tensors. II

Details Space-Times Admitting Killing-Yano Tensors. II Space-Times Admitting Killing-Yano Tensors. II

Jun 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982rspsa.381..315d&link_type=abstract

Proceedings of The Royal Society of London. Series A, Mathematical and Physical Sciences, Volume 381, Issue 1781, pp. 315-322

Physics

23

Scientific paper

In this paper we derive canonical line elements admitting a simple Killing-Yano tensor f^*ab. There exist three distinct cases according to the character of f^*ab (spacelike, timelike, null). We reveal several close analogies between the vector field l^a = f*a_rp^r along a geodesic with tangent field p^r and the angular momentum l = r x p in the case of a spacelike Killing-Yano tensor. In particular, we show that, in consequence of the Killing-Yano tensor equations, there exists an analogue of the three-dimensional position vector field in certain hypersurfaces and that l^a can be written in the form (r x p)^a. Furthermore, an analogue of the 'equatorial plane' of the classical Kepler problem can be constructed intrinsically.

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