Basic gravitational currents and Killing-Yano forms

Acik O., Ertem U., ÖNDER M. , Vercin A.

GENERAL RELATIVITY AND GRAVITATION, cilt.42, sa.11, ss.2543-2559, 2010 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 42 Konu: 11
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1007/s10714-010-1075-4
  • Sayfa Sayıları: ss.2543-2559


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.