2011/06/30 by Sergiu I. Vacaru
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Black hole (networking) #Classical mechanics #Computer science #Conserved quantity #Diagonal #Ellipsoid #General relativity #Geometry #Homogeneous space #Integrable system #Mathematical physics #Mathematics #Nonholonomic system #Nonlinear Waves and Solitons #Physics #Theoretical physics #gr-qc #hep-th #math-ph #math.MP #msc:53C15 #msc:53Z05 #msc:81T50 #msc:83C10
paper · pdf · doi:10.1140/epjc/s10052-013-2287-z
published as Eur. Phys. J. C 73 (2013) 2287 · latex2e, 11pt, 34 pages, the variant accepted by EPJC, with additional explanations, modifications and new references requested by referee
arxiv created 2013/01/09 · openalex publication_date 2013/01/31 · arxiv updated 2013/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We prove the existence of hidden symmetries in the general relativity theory defined by exact solutions with generic off-diagonal metrics, nonholonomic (non-integrable) constraints, and deformations of the frame and linear connection structure. A special role in characterization of such spacetimes is played by the corresponding nonholonomic generalizations of Stackel-Killing and Killing-Yano tensors. There are constructed new classes of black hole solutions and studied hidden symmetries for ellipsoidal and/or solitonic deformations of "prime" Kerr-Sen black holes into "target" off-diagonal metrics. In general, the classical conserved quantities (integrable and not-integrable) do not transfer to the quantized systems and produce quantum gravitational anomalies. We prove that such anomalies can be eliminated via corresponding nonholonomic deformations of fundamental geometric objects (connections and corresponding Riemannian and Ricci tensors) and by frame transforms.