Basic Gravitational Currents and Killing-Yano Forms

Details Basic Gravitational Currents and Killing-Yano Forms Basic Gravitational Currents and Killing-Yano Forms

2008-11-11

arxiv.org/abs/0811.1712v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages

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 basic 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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