Basic gravitational currents and Killing-Yano forms

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Acik Ö., Ertem U., Onder M., VERÇİN A.

GENERAL RELATIVITY AND GRAVITATION, no.11, pp.2543-2559, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2010
  • Doi Number: 10.1007/s10714-010-1075-4
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2543-2559
  • Keywords: Killing-Yano forms, Gravitational currents, Laplace-Beltrami operator, FIELDS
  • Ankara University Affiliated: Yes


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.