2008/11/11 by Özgür Açık, Ö. Açık, Ü. Ertem +4
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Conservation law #Curvature #Differential geometry #Dual polyhedron #Einstein #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Gravitation #Invariant (physics) #Manifold (fluid mechanics) #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum mechanics #Scalar (mathematics) #Scalar curvature #gr-qc #hep-th #math.DG
paper · pdf · doi:10.1007/s10714-010-1075-4
published as Gen. Relativ. Gravit., 42, 2543 (2010) · 11 pages
arxiv created 2008/11/11 · openalex publication_date 2010/08/30 · arxiv updated 2016/02/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.