Clifford and Riemann-Finsler Structures in Geometric Mechanics and Gravity
arXiv:gr-qc/0508023
Abstract
The book contains a collection of works on Riemann-Cartan and metric-affine manifolds provided with nonlinear connection structure and on generalized Finsler-Lagrange and Cartan-Hamilton geometries and Clifford structures modelled on such manifolds. The choice of material presented has evolved from various applications in modern gravity and geometric mechanics and certain generalizations to noncommutative Riemann-Finsler geometry. The authors develop and use the method of anholonomic frames with associated nonlinear connection structure and apply it to a number of concrete problems: constructing of generic off-diagonal exact solutions, in general, with nontrivial torsion and nonmetricity, possessing noncommutative symmetries and describing black ellipsoid/torus configurations, locally anisotropic wormholes, gravitational solitons and warped factors and investigation of stability of such solutions; classification of Lagrange/ Finsler -- affine spaces; definition of nonholonomic Dirac operators and their applications in commutative and noncommutative Finsler geometry.
Accepted by Geometry Balkan Press, 693 pages + 3 eps figures, version 2 with minor modifications, new affiliation and Preface by M. Anastasiei
Cited by in corpus (43)
- Resembling dark energy and modified gravity with Finsler-Randers cosmology
- Principles of Einstein-Finsler Gravity and Perspectives in Modern Cosmology
- Friedmann Robertson-Walker model in generalised metric space-time with weak anisotropy
- Emergent Models for Gravity: an Overview of Microscopic Models
- Black Strings from Minimal Geometric Deformation in a Variable Tension Brane-World
- Spectral Functionals, Nonholonomic Dirac Operators, and Noncommutative Ricci Flows
- Cosmological equivalence between the Finsler-Randers space-time and the DGP gravity model
- Fractional Dynamics from Einstein Gravity, General Solutions, and Black Holes
- Cyclic and Ekpyrotic Universes in Modified Finsler Osculating Gravity on Tangent Lorentz Bundles
- Black string corrections in variable tension braneworld scenarios
- Finsler Black Holes Induced by Noncommutative Anholonomic Distributions in Einstein Gravity
- Fedosov Quantization of Lagrange-Finsler and Hamilton-Cartan Spaces and Einstein Gravity Lifts on (Co) Tangent Bundles
- Deformation Quantization of Almost Kahler Models and Lagrange-Finsler Spaces
- Critical Remarks on Finsler Modifications of Gravity and Cosmology by Zhe Chang and Xin Li
- Notes on the Two-brane Model with Variable Tension
- Einstein Gravity as a Nonholonomic Almost Kahler Geometry, Lagrange-Finsler Variables, and Deformation Quantization
- Spacetime and observer space symmetries in the language of Cartan geometry
- A unified description for dipoles of the fine-structure constant and SnIa Hubble diagram in Finslerian universe
- CPT-Violating Leptogenesis induced by Gravitational Defects
- Weak field equations and generalized FRW cosmology on the tangent Lorentz bundle
- A Finslerian version of 't Hooft Deterministic Quantum Models
- Dark Gravitational Sectors on a Generalized Scalar-Tensor Vector Bundle Model and Cosmological Applications
- Schwarzschild-Finsler-Randers spacetime: Dynamical analysis, Geodesics and Deflection Angle
- Applications of the Schwarzschild-Finsler-Randers model
- New Classes of Off-Diagonal Cosmological Solutions in Einstein Gravity
- Einstein Gravity in Almost Kahler Variables and Stability of Gravity with Nonholonomic Distributions and Nonsymmetric Metrics
- Broken Scale Invariance, Gravity Mass, and Dark Energy in Modified Einstein Gravity with Two Measure Finsler Like Variables
- Loop Quantum Gravity in Ashtekar and Lagrange-Finsler Variables and Fedosov Quantization of General Relativity
- Gravitational Field on the Lorentz Tangent Bundle: Generalized Paths and Field Equations
- Quasi-Stationary Solutions in Gravity Theories with Modified Dispersion Relations and Finsler-Lagrange-Hamilton Geometry
- Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics
- Two-branes with variable tension model and the effective Newtonian constant
- Volume forms for time orientable Finsler spacetimes
- Nonassociative geometry of nonholonomic phase spaces with star R-flux string deformations and (non) symmetric metrics
- Anisotropic Conformal Dark Gravity on the Lorentz Tangent Bundle Spacetime
- Nonholonomic Black Ring and Solitonic Solutions in Finsler and Extra Dimension Gravity Theories
- Spinor and Twistor Geometry in Einstein Gravity and Finsler Modifications
- Pati-Salam model in curved space-time from square root Lorentz manifold
- A note on Clifford bundles and certain Finsler type spaces
- Transverse geometry and physical observers
- Nonlinear connections and 1+3 splittings of spacetime
- Frobenius Curvature, Electromagnetic Strain and Description of Photon-like Objects
- On electromagnetism and generalized energy-momentum tensor of the electromagnetic field in spaces with Finsler geometry