Basic gravitational currents and Killing-Yano forms


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

GENERAL RELATIVITY AND GRAVITATION, vol.42, no.11, pp.2543-2559, 2010 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 11
  • Publication Date: 2010
  • Doi Number: 10.1007/s10714-010-1075-4
  • Title of Journal : GENERAL RELATIVITY AND GRAVITATION
  • Page Numbers: pp.2543-2559

Abstract

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.