Basic Gravitational Currents and Killing-Yano Forms

Abstract

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.

11 pages

References in corpus (5)

• `Hidden' Symmetries of Higher Dimensional Rotating Black Holes
• Conserved gravitational charges from Yano tensors
• First-order symmetries of Dirac equation in curved background: a unified dynamical symmetry condition
• Conformal Killing forms on Riemannian manifolds
• Gravitational charges of transverse asymptotically AdS spacetimes

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• Generalized symmetry superalgebras
• Couplings of gravitational currents with Chern-Simons gravities
• Harmonic spinors from twistors and potential forms
• Twistors from Killing Spinors alias Radiation from Pair Annihilation I: Theoretical Considerations
• Spin-1/2 and spin-3/2 field solutions in plane wave spacetimes
• Spin Geometry and Some Applications
• Algebra structure of conformal Killing-Yano forms in geometries with skew-symmetric torsion
• Rigidity of Killing-Yano and conformal Killing-Yano superalgebras