https://neckpinch.com/authors/laurentiu-bubuianu/New arXiv papers by Laurenţiu Bubuianu, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2410.03700arxiv:2410.03700Tue, 24 Sep 2024 00:00:00 GMTL. Bubuianu, E. Nurlan, J. O. Seti, S. Vacaru, E. V. Veliev — We elaborate on nonmetric geometric flow theory and metric-affine gravity with applications in modern cosmology. Two main motivations for our research follow from the facts that 1) cosmological models for f(Q) modified gravity theories, MGTs, are efficient for describing recent observational data provided by the James Webb Space Telescope; and 2) the statistical thermodynamic properties of such nonmetric locally anisotropic cosmological models can be studied using generalizations of the concept of G. Perelman entropy. We derive nonmetric distorted R. Hamilton and Ricci soliton equations in such canonical nonholonomic variables when corresponding systems of nonlinear PDEs can be decoupled and integrated in general off-diagonal forms. This is possible if we develop and apply the anholonomic frame and connection deformation method involving corresponding types of generating functions and generating sources encoding nonmetric distortions. Using such generic off-diagonal solutions (when the coefficients of metrics and connections may depend generically on all spacetime coordinates), we model accelerating cosmological scenarios with quasi-periodic gravitational and (effective) matter fields; and study topological and nonlinear geometric properties of respective dark energy and dark matter, DE and DM, models. As explicit examples, we analyze some classes of nonlinear symmetries defining topological quasicrystal, QC, phases which can modified to generate other types of quasi-periodic and locally anisotropic structures. The conditions when such nonlinear systems possess a behaviour which is similar to that of the Lambda cold dark matter (ΛCDM) scenario are stated. We conclude that nonmetric geometric and cosmological flows can be considered as an alternative to the ΛCDM concordance models and speculate on how such theories can be elaborated.Anisotropic & nonlocal flowsRicci solitonsPerelman entropyPhysics https://arxiv.org/abs/2410.03698arxiv:2410.03698Tue, 24 Sep 2024 00:00:00 GMTL. Bubuianu, J. O. Seti, S. Vacaru, E. V. Veliev — We elaborate on a model of nonassociative and noncommutative gauge gravity for the de Sitter gauge group SO(4,1) embedding extensions of the affine structure group Af(4,1) and the Poincaré group ISO(3,1). In string theory, such nonassociative gauge gravity theories are determined by star product R-flux deformations. They are new avenues to quantum gravity and geometric and quantum information theories. We analyze physically important and geometric thermodynamic properties of new classes of generic off-diagonal cosmological solitonic solutions encoding nonassociative effective sources. Particularly, we focus on modelling by such solutions of locally anisotropic and inhomogeneous dark matter and dark energy structures generated as nonassociative solitonic hierarchies. Such accelerating cosmological evolution scenarios can't be described in the framework of the Bekenstein-Hawking thermodynamic formalism. This motivates a change in the gravitational thermodynamic paradigm by considering nonassociative and relativistic generalizations of the concept of W-entropy in the theory of Ricci flows. Finally, we compute the corresponding modified G. Perelman's thermodynamic variables and analyze the temperature-like evolution of cosmological constants determined by nonassociative cosmological flows.Ricci flowPerelman entropyHomogeneous spacesPhysics https://arxiv.org/abs/2402.19362arxiv:2402.19362Thu, 29 Feb 2024 00:00:00 GMTLaurenţiu Bubuianu, Sergiu I. Vacaru, Elşen Veli Veliev, Assel Zhamysheva — We extend the anholonomic frame and connection deformation method, AFCDM, for constructing exact and parametric solutions in general relativity, GR, to geometric flow models and modified gravity theories, MGTs, with nontrivial torsion and nonmetricity fields. Following abstract geometric or variational methods, we can derive corresponding systems of nonmetric gravitational and matter field equations which consist of very sophisticated systems of coupled nonlinear PDEs. Using nonholonomic frames with dyadic spacetime splitting and applying the AFCDM, we prove that such systems of PDEs can be decoupled and integrated in general forms for generic off-diagonal metric structures and generalized affine connections. We generate new classes of quasi-stationary solutions (which do not depend on time like coordinates) and study the physical properties of some physically important examples. Such exact or parametric solutions are determined by nonmetric solitonic distributions and/or ellipsoidal deformations of wormhole hole configurations. It is not possible to describe the thermodynamic properties of such solutions in the framework of the Bekenstein-Hawking paradigm because such metrics do not involve, in general, certain horizons, duality, or holographic configurations. Nevertheless, we can always elaborate on associated Grigori Perelman thermodynamic models elaborated for nonmetric geometric flows. In explicit form, applying the AFCDM, we construct and study the physical implications of new classes of traversable wormhole solutions describing solitonic deformation and dissipation of non-Riemannian geometric objects. Such models with nontrivial gravitational off-diagonal vacuum are important for elaborating models of dark energy and dark matter involving wormhole configurations and solitonic-type structure formation.Ricci flowPhysics https://arxiv.org/abs/2402.10993arxiv:2402.10993Fri, 16 Feb 2024 00:00:00 GMTLaurenţiu Bubuianu, Douglas Singleton, Sergiu I. Vacaru, Elşen Veli Veliev — This article consists of an introduction to the theory of nonassociative geometric classical and quantum information flows defined by star products with R-flux deformations in string gravity. Corresponding nonassociative generalizations of the concepts of classical Shannon entropy, quantum von Neumann entropy, Rényi entropy are formulated. The fundamental geometric and quantum information objects are computed following the Grigori Perelman statistical thermodynamic approach to Ricci flows and gravity theories generalized for phase spaces modelled as (co) tangent Lorentz bundles. Nonassociative parametric deformations and nonholonomic thermo-geometric versions of statistical generating functions, their quantum analogues as density matrices are considered for deriving the entropy, energy and fluctuation functionals. This allows us to define and compute respective classical and quantum relative and conditional entropies, mutual information and nonassociative entanglement and thermodynamic information variables. We formulate the principles of nonassociative quantum geometric and information flow theory, QGIF, and study the basic properties of such quasi-stationary models related to modified gravity theories. Applications are considered for nonassociative deformed and entangled couples of four-dimensional, 4-d, wormholes (defined by respective spacetime and/or momentum type coordinates) and nonassociative QGIFs of 8-d phase space generalized wormholes configurations. Finally, we speculate on phase space black holes and wormholes being transversable for nonassociative qubits, quantum channels and entanglement witness; thought and laboratory experiments are discussed; and perspectives for quantum computer modelling and tests of nonassociative geometric flow and gravity theories are considered.Ricci flow4-manifoldsPhysics