Nonassociative Ricci flows, star product and R-flux deformed black holes, and swampland conjectures

Abstract

We extend to a theory of nonassociative geometric flows a string-inspired model of nonassociative gravity determined by star product and R-flux deformations. The nonassociative Ricci tensor and curvature scalar defined by (non) symmetric metric structures and generalized (non) linear connections are used for defining nonassociative versions of Grigori Perelman F- and W-functionals for Ricci flows and computing associated thermodynamic variables. We develop and apply the anholonomic frame and connection deformation method, AFCDM, which allows us to construct exact and parametric solutions describing nonassociative geometric flow evolution scenarios and modified Ricci soliton configurations with quasi-stationary generic off-diagonal metrics. There are provided explicit examples of solutions modelling geometric and statistical thermodynamic evolution on a temperature-like parameter of modified black hole configurations encoding nonassociative star-product and R-flux deformation data. Further perspectives of the paper are motivated by nonassociative off-diagonal geometric flow extensions of the swampland program, related conjectures and claims on geometric and physical properties of new classes of quasi-stationary Ricci flow and black hole solutions.

arXiv comment81 pages latex2e 11pt, v1 accepted to Fort. der Physik, FP; 5th partner work to arXiv: 2106.01320, 2106.01869, 2108.04689,2207.05157 published in FP, FP, EPJC, JHEP

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• Dark energy and dark matter configurations for wormholes and solitionic hierarchies of nonmetric Ricci flows and $F(R,T,Q,T_m)$ gravity
• Nonassociative gauge gravity theories with R-flux star products and Batalin-Vilkovisky quantization in algebraic quantum field theory
• 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
• Nonassociative Einstein-Dirac-Maxwell systems and R-flux modified Reissner-Nordström black holes and wormholes
• Nonmetric geometric flows and quasicrystalline topological phases for dark energy and dark matter in $f(Q)$ cosmology
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• General off-diagonal integrability of metric and nonmetric geometric flow and Finsler-Lagrange-Hamilton modified Einstein equations