A Rainich-like approach to the Killing-Yano tensors

Details A Rainich-like approach to the Killing-Yano tensors A Rainich-like approach to the Killing-Yano tensors

2002-12-20

arxiv.org/abs/gr-qc/0212085v2

Gen. Rel. Grav. 35 (2002) 1191

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

19 pages, 0 figures

Scientific paper

The Rainich problem for the Killing-Yano tensors posed by Collinson \cite{col} is solved. In intermediate steps, we first obtain the necessary and sufficient conditions for a 2+2 almost-product structure to determine the principal 2--planes of a skew-symmetric Killing-Yano tensor and then we give the additional conditions on a symmetric Killing tensor for it to be the square of a Killing-Yano tensor.We also analyze a similar problem for the conformal Killing-Yano and the conformal Killing tensors. Our results show that, in both cases, the principal 2--planes define a maxwellian structure. The associated Maxwell fields are obtained and we outline how this approach is of interest in studying the spacetimes that admit these kind of first integrals of the geodesic equation.

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