Anholonomic Frames, Generalized Killing Equations, and Anisotropic Taub NUT Spinning Spaces

Abstract

By using anholonomic frames in (pseudo) Riemannian spaces we define anisotropic extensions of Euclidean Taub-NUT spaces. With respect to coordinate frames such spaces are described by off-diagonal metrics which could be diagonalized by corresponding anholonomic transforms. We define the conditions when the 5D vacuum Einstein equations have as solutions anisotropic Taub-NUT spaces. The generalized Killing equations for the configuration space of anisotropically spinning particles (anisotropic spinning space) are analyzed. Simple solutions of the homogeneous part of these equations are expressed in terms of some anisotropically modified Killing-Yano tensors. The general results are applied to the case of the four-dimensional locally anisotropic Taub-NUT manifold with Euclidean signature. We emphasize that all constructions are for(pseudo) Riemannian spaces defined by vacuum soltions, with generic anisotropy, of 5D Einstein equations, the solutions being generated by applying the moving frame method.

Version 4, published

References in corpus (28)

• A Large Mass Hierarchy from a Small Extra Dimension
• An Alternative to Compactification
• The Hierarchy Problem and New Dimensions at a Millimeter
• New Dimensions at a Millimeter to a Fermi and Superstrings at a TeV
• Phenomenology, Astrophysics and Cosmology of Theories with Sub-Millimeter Dimensions and TeV Scale Quantum Gravity
• SUSY in the sky
• Stabilization of Sub-Millimeter Dimensions: The New Guise of the Hierarchy Problem
• Supersymmetry and the Geometry of Taub-NUT
• Wormholes and Flux Tubes in 5D Kaluza-Klein Theory
• Spinors in Higher Dimensional and Locally Anisotropic Spaces
• Superstrings in Higher Order Extensions of Finsler Superspaces
• Anholonomic Soliton-Dilaton and Black Hole Solutions in General Relativity
• Gauge and Einstein Gravity from Non-Abelian Gauge Models on Noncommutative Spaces
• Locally Anisotropic Gravity and Strings
• Locally Anisotropic Kinetic Processes and Thermodynamics in Curved Spaces
• Killing tensors and a new geometric duality
• Spinning particles in Taub-NUT space
• Dirac Spinor Waves and Solitons in Anisotropic Taub-NUT Spaces
• Locally Anisotropic Wormholes and Flux Tubes in 5D Gravity
• Generalized Runge-Lenz Vector in Taub-Nut Spinning Space
• Multidimensional Geometrical Model of the Renormalized Electrical Charge with Splitting off the Extra Coordinates
• Supersymmetries and constants of motion in Taub-NUT spinning space
• Generalized Killing equations and Taub-NUT spinning space
• The Dirac equation in Taub-NUT space
• The Geodesic Motion in Taub-Nut Spinning Space
• Flux Tube Solution in 5D Kaluza-Klein Theory
• Spinors and Field Interactions in Higher Order Anisotropic Spaces
• Multidimensional Gravity on the Principal Bundles

Cited by in corpus (20)

• Exact Solutions with Noncommutative Symmetries in Einstein and Gauge Gravity
• Finsler and Lagrange Geometries in Einstein and String Gravity
• Fractional Dynamics from Einstein Gravity, General Solutions, and Black Holes
• Off-Diagonal Deformations of Kerr Black Holes in Einstein and Modified Massive Gravity and Higher Dimensions
• Parametric Nonholonomic Frame Transforms and Exact Solutions in Gravity
• Frenkel electron on an arbitrary electromagnetic background and magnetic Zitterbewegung
• Clifford-Finsler Algebroids and Nonholonomic Einstein-Dirac Structures
• Warped, Anisotropic Wormhole/Soliton Configurations in Vacuum 5D Gravity
• Lagrange-Fedosov Nonholonomic Manifolds
• Warped Solitonic Deformations and Propagation of Black Holes in 5D Vacuum Gravity
• Locally Anisotropic Structures and Nonlinear Connections in Einstein and Gauge Gravity
• Ricci Flows and Solitonic pp--Waves
• Heterotic Supergravity with Internal Almost-Kähler Spaces, Instantons for $SO(32)$, or $E_8\times E_8$, Gauge Groups, and Deformed Black Holes with Soliton, Quasiperiodic and/or Pattern-forming Structures
• Modified Dynamical Supergravity Breaking and Off-Diagonal Super-Higgs Effects
• Nonholonomic Ricci Flows and Running Cosmological Constant: I. 4D Taub-NUT Metrics
• Off-Diagonal Deformations of Kerr Metrics and Black Ellipsoids in Heterotic Supergravity
• Hidden Symmetries for Ellipsoid-Solitonic Deformations of Kerr-Sen Black Holes and Quantum Anomalies
• Nonlinear Connections and Nearly Autoparallel Maps in General Relativity
• The Anholonomic Frame and Connection Deformation Method for constructing off-diagonal solutions in (modified) Einstein gravity and nonassociative geometric flows and Finsler-Lagrange-Hamilton theories
• General off-diagonal integrability of metric and nonmetric geometric flow and Finsler-Lagrange-Hamilton modified Einstein equations