Basic gravitational currents and Killing-Yano forms

Details Basic gravitational currents and Killing-Yano forms Basic gravitational currents and Killing-Yano forms

Nov 2010

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010gregr..42.2543a&link_type=abstract

General Relativity and Gravitation, Volume 42, Issue 11, pp.2543-2559

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Killing–Yano Forms, Gravitational Currents, Laplace–Beltrami Operator

Scientific paper

It has been shown that for each Killing-Yano (KY)-form accepted by an n-dimensional (pseudo)Riemannian manifold of arbitrary signature, two different gravitational currents can be defined. Conservation of the currents are explicitly proved by showing co-exactness of the one and co-closedness of the other. Some general geometrical facts implied by these conservation laws are also elucidated. In particular, the conservation of the one-form currents implies that the scalar curvature of the manifold is a flow invariant for all of its Killing vector fields. It also directly follows that, while all KY-forms and their Hodge duals on a constant curvature manifold are the eigenforms of the Laplace-Beltrami operator, for an Einstein manifold this is certain only for KY 1-forms, ( n - 1)-forms and their Hodge duals.

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