Nonassociative geometry of nonholonomic phase spaces with star R-flux string deformations and (non) symmetric metrics

Abstract

We elaborate on nonassociative differential geometry of phase spaces endowed with nonholonomic (non-integrable) distributions and frames, nonlinear and linear connections, symmetric and nonsymmetric metrics, and correspondingly adapted quasi-Hopf algebra structures. The approach is based on the concept of nonassociative star product introduced for describing closed strings moving in a constant R-flux background. Generalized Moyal-Weyl deformations are considered when, for nonassociative and noncommutative terms of star deformations, there are used nonholonomic frames (bases) instead of local partial derivatives. In such modified nonassociative and nonholonomic spacetimes and associated complex/ real phase spaces, the coefficients of geometric and physical objects depend both on base spacetime coordinates and conventional (co) fiber velocity/ momentum variables like in (non) commutative Finsler-Lagrange-Hamilton geometry. For nonassociative and (non) commutative phase spaces modelled as total spaces of (co) tangent bundles on Lorentz manifolds enabled with star products and nonholonomic frames, we consider associated nonlinear connection, N-connection, structures determining conventional horizontal and (co) vertical (for instance, 4+4) splitting of dimensions and N-adapted decompositions of fundamental geometric objects. There are defined and computed in abstract geometric and N-adapted coefficient forms the torsion, curvature and Ricci tensors. We extend certain methods of nonholonomic geometry in order to construct R-flux deformations of vacuum Einstein equations for the case of N-adapted linear connections and symmetric and nonsymmetric metric structures.

latex2e, 69 pages, v2 with small typos corrections and updated reference comparing to v1, v3 is equivalent to the published version

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Cited by in corpus (6)

• Nonassociative geometric and quantum information flows and R-flux deformations of wormhole solutions in string gravity
• Nonassociative black holes in R-flux deformed phase spaces and relativistic models of G. Perelman thermodynamics
• Nonassociative Ricci flows, star product and R-flux deformed black holes, and swampland conjectures
• Nonassociative black ellipsoids distorted by R-fluxes and four dimensional thin locally anisotropic accretion disks
• Nonassicative cosmological solitonic R-flux deformations in gauge gravity and G. Perelman geometric flow thermodynamics
• 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