Decoupling and integrability of nonassociative vacuum phase space gravitational equations with star and R-flux parametric deformations

Abstract

We prove that nonassociative star deformed vacuum Einstein equations can be decoupled and integrated in certain general forms on phase spaces involving real R-flux terms induced as parametric corrections on base Lorentz manifold spacetimes. The geometric constructions are elaborated with parametric (on respective Planck, $\hslash$, and string, $\kappa :={\ell }_s^3/6\hslash$, constants) and nonholonomic dyadic decompositions of fundamental geometric and physical objects. This is our second partner work on elaborating nonassociative geometric and gravity theories with symmetric and nonsymmetric metrics, (non) linear connections, star deformations defined by generalized Moyal-Weyl products, endowed with quasi-Hopf algebra, or other type algebraic and geometric structures, and all adapted to nonholonomic distributions and frames. We construct exact and parametric solutions for nonassociative vacuum configurations (with nontrivial or effective cosmological constants) defined by star deformed generic off-diagonal (non) symmetric metrics and (generalized) nonlinear and linear connections. The coefficients of geometric objects defining such solutions are determined by respective classes of generating and integration functions and constants and may depend on all phase space coordinates [spacetime ones, $(x^i,t)$; and momentum like variables, $(p_a,E$)]. Quasi-stationary configurations are stated by solutions with spacetime Killing symmetry on a time like vector ${\partial }_t$ but with possible dependencies on momentum like coordinates on star deformed phase spaces.

latex2e, 11pt, 68 pages, 2d partner work; v2 with minor typos correction and updated references comparing to v1, arXiv:submit/3646742 from March 12, 2021

References in corpus (4)

• Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes
• Nonholonomic Ricci Flows, Exact Solutions in Gravity, and Symmetric and Nonsymmetric Metrics
• Einstein Gravity in Almost Kahler Variables and Stability of Gravity with Nonholonomic Distributions and Nonsymmetric Metrics
• 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

Cited by in corpus (11)

• 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 black ellipsoids distorted by R-fluxes and four dimensional thin locally anisotropic accretion disks
• Nonassociative gauge gravity theories with R-flux star products and Batalin-Vilkovisky quantization in algebraic quantum field theory
• Nonassociative Ricci flows, star product and R-flux deformed black holes, and swampland conjectures
• Nonassociative Einstein-Dirac-Maxwell systems and R-flux modified Reissner-Nordström black holes and wormholes
• 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
• Off-diagonal deformations of regular Schwarzschild black holes and general relativistic G. Perelman thermodynamics
• The fundamental physical importance of generic off-diagonal solutions and Grigori Perelman entropy in the Einstein gravity theory
• Asymptotic safe nonassociative quantum gravity with star R-flux products, Goroff-Sagnotti counter-terms, and geometric flows
• General off-diagonal integrability of metric and nonmetric geometric flow and Finsler-Lagrange-Hamilton modified Einstein equations