arXiv subjects

Sergiu I. Vacaru

Publications and source records attributed to Sergiu I. Vacaru.

At least 19 recordsLinked to original sources

arXiv2026

Off-diagonal solutions in Einsteingravity modeling f(R) gravity and dynamical darkenergy vs Lambda CDM cosmology

Modified gravity theories (MGTs) have long been studied as alternatives to general relativity (GR) and the standard Lambda CDM cosmological model. For example, exponential f(R) models often yield better fits to observational data, suggesting that Lambda CDM may be inadequate. In this work, we argue that the gravitational and accelerating cosmology paradigm can remain close to GR and Lambda CDM if one considers broader classes of off-diagonal cosmological solutions of the Einstein equations. These solutions are constructed using the anholonomic frame and connection deformation method (AFCDM), which enables the decoupling and integration of nonlinear systems of partial differential equations in nonholonomic dyadic variables with connection distortions. The resulting off-diagonal Einstein manifolds and cosmological models are characterized by nonholonomic constraints, nonlinear symmetries, and effective cosmological constants. Such structures allow one to approximate cosmological effects, mimic features of MGTs, and describe gravitational polarization, local anisotropies, and dark energy and dark matter phenomena within GR.

physics.gen-ph↗

arXiv2026

General off-diagonal integrability of metric and nonmetric geometric flow and Finsler-Lagrange-Hamilton modified Einstein equations

Over the last seventy years, many Finsler-type geometric and modified gravity theories have been elaborated. They have been formulated in terms of different classes of Finsler generating functions, metric and nonmetric structures, nonlinear and linear connections, and various sets of postulated fundamental geometric objects with corresponding nonholonomic dynamical or evolution equations. In several approaches, the resulting gravitational and matter field equations were not completely defined geometrically, or were developed only for restricted models. We present a progress report with historical remarks and a summary of new results on Finsler - Lagrange - Hamilton geometric flow and gravity theories. Such theories can be constructed in an axiomatic form on (co) tangent Lorentz bundles as nontrivial modifications of Einstein gravity.

math-ph↗

arXiv2026

Batalin-Fradkin-Vilkovisky quantization of Einstein gravity with off-diagonal solutions encoding Hořava type generating functions

We develop and apply the Batalin-Fradkin-Vilkovisky (BFV) formalism for quantizing off-diagonal solutions of the Einstein equations in general relativity. In the quasi-classical limit of quantum gravity, such solutions possess specific nonlinear symmetries and encode Hořava - Lifshitz (HL) configurations with anisotropic scaling and effective cosmological constants. The geometric constructions are performed on Lorentz manifolds enabled with nonholonomic 2+2 and 3+1 fibration structures.

gr-qc↗

arXiv2025

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

This article is a status report on the Anholonomic Frame and Connection Deformation Method, AFCDM, for constructing generic off-diagonal exact and parametric solutions in general relativity, GR, relativistic geometric flows, and modified gravity theories, MGTs. Such models can be generalized to nonassociative and noncommutative star products on phase spaces and modelled equivalently as nonassociative Finsler-Lagrange-Hamilton geometries. Our approach involves a nonholonomic geometric reformulation of classical models of gravitational and matter fields described by Lagrange and Hamilton densities on relativistic phase spaces. Using nonholonomic dyadic variables, the Einstein equations in GR and MGTs can be formulated as systems of nonlinear partial differential equations(PDEs), which can be decoupled and integrated in some general off-diagonal forms. In this approach, the Lagrange and Hamilton dynamics and related models of classical and quantum evolution are equivalently described in terms of generalized Finsler-like or canonical metrics and (nonlinear) connection structures on deformed phase spaces defined by solutions of modified Einstein equations. New classes of exact and parametric solutions in (nonassociative) MGTs are formulated in terms of generating and integration functions and generating effective/ matter sources. The physical interpretation of respective classes of solutions depends on the type of (non) linear symmetries, prescribed boundary/ asymptotic conditions, or posed Cauchy problems.

gr-qc↗

arXiv2025

The fundamental physical importance of generic off-diagonal solutions and Grigori Perelman entropy in the Einstein gravity theory

The gravitational field equations in general relativity (GR) consist of a sophisticated system of nonlinear partial differential equations. Solving such equations in some generic off-diagonal forms is usually a hard analytic or numeric task. Physically important solutions in GR were constructed using a diagonal ansatz for metrics with a maximum of 4 independent coefficients. The Einstein equations can be solved in exact or parametric forms determined by some integration constants for corresponding assumptions on spherical or cylindrical spacetime symmetries. The anholonomic frame and connection deformation method allows us to construct generic off-diagonal solutions described by 6 independent coefficients of metrics depending, in general, on all spacetime coordinates. New types of exact and parametric solutions are determined by generating and integration functions and (effective) generating sources. They may describe vacuum gravitational and matter fields solitonic hierarchies; locally anisotropic polarizations of physical constants for black holes, wormholes, black toruses, or cosmological solutions; various types of off-diagonal deformations of horizons, etc. The additional degrees of freedom (related to off-diagonal coefficients) can be used to describe dark energy and dark matter configurations and elaborate locally anisotropic cosmological scenarios. In general, the generic off-diagonal solutions do not involve certain hypersurface or holographic configurations and can't be described in the framework of the Bekenstein-Hawking thermodynamic paradigm. We argue that generalizing the concept of G. Perelman's entropy for relativistic Ricci flows allows us to define and compute geometric thermodynamic variables for all possible classes of solutions in GR.

gr-qc↗

arXiv2025

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

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.

physics.gen-ph↗

arXiv2025

Off-diagonal deformations of regular Schwarzschild black holes and general relativistic G. Perelman thermodynamics

We construct new classes of solutions describing generic off-diagonal deformations of regular Schwarzschild black holes (BHs) in general relativity (GR). Examples of such (primary) diagonal metrics reducing the Einstein equations to integrable systems of nonlinear ordinary differential equations were studied in a recent work by R. Casadio, A. Kamenshchik and J. Ovalle in Phys. Rev. D 111 (2025) 064036. We develop and apply our anholonomic frame and connection deformations method, which allows us to generate new classes of target off-diagonal solutions. Ansatz that reduces the gravitational field equations to systems of (exactly or parametric) integrable systems of nonlinear partial differential equations are used. We find and analyze certain families of deformed regular BHs containing an off-diagonal de Sitter condensate encoding solitonic vacuum configurations, with possible deformations of horizons and/or gravitational polarizations of constants. We emphasize that general off-diagonal solutions do not involve certain hypersurface or holographic configurations. This means that the Bekenstein-Hawking thermodynamic paradigm is not applicable for characterizing the physical properties of such target regular solutions. We argue that the concept of G. Perelman's entropy and relativistic geometric flow thermodynamics is more appropriate. Using nonlinear symmetries involving effective cosmological constants, we show how to compute thermodynamic variables for various classes of physically essential solutions in GR.

physics.gen-ph↗

arXiv2025

Inconsistencies of nonmetric Einstein-Dirac-Maxwell theories and a cure for geometric flows of f(Q) black ellipsoid, toroid and wormhole solutions

Many papers on modified gravity theories (MGTs), and metric-affine geometry have been published. New classes of black hole (BH), wormhole (WH), and cosmological solutions involving nonmetricity and torsion fields were constructed. Nevertheless, the fundamental problems of formulating nonmetric Einstein-Dirac-Maxwell (EDM), equations, and studying important nonmetric gravitational, electromagnetic and fermion effects have not been solved in MGTs. The main goal of this work is to elaborate on a model of nonmetric EDM theory as a generalisation of f(Q) gravity. We develop our anholonomic frame and connection deformation method, which allows us to decouple in a general form and integrate nonmetric gravitational and matter field equations. New classes of generated quasi-stationary solutions are defined by effective sources with Dirac and Maxwell fields, nonmetricity and torsion fields, and generating functions depending, in general, on all space-time coordinates. For respective nonholonomic parameterisations, such solutions describe nonmetric EDM deformations of BH and cosmological metrics. Variants of nonmetric BH, WH and toroid solutions with locally anisotropic polarisations of the gravitational vacuum, masses of fermions, and effective electromagnetic sources are constructed and analysed. Such nonmetric deformed physical objects can't be characterised in the framework of the Bekenstein-Hawking paradigm if certain effective horizon/ holographic configurations are not involved. We show how to define and compute other types of nonmetric geometric thermodynamic variables using generalisations of the concept of G. Perelman W-entropy.

physics.gen-ph↗

arXiv2024

Nonassociative gauge gravity theories with R-flux star products and Batalin-Vilkovisky quantization in algebraic quantum field theory

Nonassociative modifications of general relativity, GR, and quantum gravity, QG, models naturally arise as star product and R-flux deformations considered in string/ M-theory. Such nonassociative and noncommutative geometric and quantum information theories were formulated on phase spaces defined as cotangent Lorentz bundles enabled with nonassociative symmetric and nonsymmetric metrics and nonlinear and linear connection structures. We outline the analytic methods and proofs that corresponding geometric flow evolution and dynamical field equations can be decoupled and integrated in certain general off-diagonal forms. New classes of solutions describing nonassociative black holes, wormholes, and locally anisotropic cosmological configurations are constructed using such methods. We develop the Batalin-Vilkovisky, BV, formalism for quantizing modified gravity theories, MGTs, involving twisted star products and semi-classical models of nonassociative gauge gravity with de Sitter/affine/ Poincaré double structure groups. Such theories can be projected on Lorentz spacetime manifolds in certain forms equivalent to GR or MGTs with torsion generalizations etc. We study the properties of the classical and quantum BV operators for nonassociative phase spaces and nonassociative gauge gravity. Recent results and methods from algebraic QFT are generalized to involve nonassociative star product deformations of the anomalous master Ward identity. Such constructions are elaborated in a nonassociative BV perspective and for developing non-perturbative methods in QG.

hep-th↗

arXiv2024

Dark energy and dark matter configurations for wormholes and solitionic hierarchies of nonmetric Ricci flows and $F(R,T,Q,T_{m})$ gravity

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.

gr-qc↗

arXiv2024

Nonassociative geometric and quantum information flows and R-flux deformations of wormhole solutions in string gravity

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.

hep-th↗

arXiv2023

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

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.

physics.gen-ph↗

arXiv2022

Quantum geometric information flows and relativistic generalizations of G. Perelman thermodynamics for nonholonomic Einstein systems with black holes and stationary solitonic hierarchies

We investigate classical and quantum geometric information flow theories (respectively, GIFs and QGIFs) when the geometric flow evolution and field equations for nonholonomic Einstein systems, NES, are derived from Perelman-Lyapunov type entropic type functionals. In this work, the term NES encodes models of gravitational and matter fields interactions and their geometric flow evolution subjected to nonholonomic (equivalently, non-integrable, anholonomic) constraints. There are used canonical geometric variables which allow a general decoupling and integration of systems of nonlinear partial differential equations describing GIFs and QGIFs and (for self-similar geometric flows) Ricci soliton type configurations. Our approach is different from the methods and constructions elaborated for special classes of solutions characterized by area--hypersurface entropy, related holographic and dual gauge--gravity models, and conformal field theories, involving generalizations of the Bekenstein-Hawking entropy and black hole thermodynamics. We formulate the theory of QGIFs which in certain quasi-classical limits encodes GIFs and models with flow evolution of NES. There are analysed the most important properties (inequalities) for NES and defined and computed QGIF versions of the von Neumann, relative and conditional entropy; mutual information, (modified) entanglement and Rényi entropy. We construct explicit examples of generic off-diagonal exact and parametric solutions describing stationary solitonic gravitational hierarchies and deformations of black hole configurations. Finally, we show how Perelman's entropy and geometric thermodynamic values, and extensions to GIF and QGIF models can be computed for various new classes of exact solutions which cannot be described following the Bekenstein-Hawking approach.

physics.gen-ph↗

arXiv2021

Nonassociative black ellipsoids distorted by R-fluxes and four dimensional thin locally anisotropic accretion disks

We construct nonassociative quasi-stationary solutions describing deformations of Schwarzschild black holes, BHs, to ellipsoid configurations, which can be black ellipsoids, BEs, and/or BHs with ellipsoidal accretion disks. Such solutions are defined by generic off-diagonal symmetric metrics and nonsymmetric components of metrics (which are zero on base four dimensional, 4-d, Lorentz manifold spacetimes but nontrivial in respective 8-d total (co) tangent bundles). Distorted nonassociative BH and BE solutions are found for effective real sources with terms proportional to $\hbar κ$ (for respective Planck and string constants). These sources and related effective nontrivial cosmological constants are determined by nonlinear symmetries and deformations of the Ricci tensor by nonholonomic star products encoding R-flux contributions from string theory. To generate various classes of (non) associative / commutative distorted solutions we generalize and apply the anholonomic frame and connection deformation method for constructing exact and parametric solutions in modified gravity and/or general relativity theories. We study properties of locally anisotropic relativistic, optically thick, could and thin accretion disks around nonassociative distorted BHs, or BEs, when the effects due to the rotation are negligible. Such configurations describe angular anisotropic deformations of axially symmetric astrophysical models when the nonassociative distortions are related to the outer parts of the accretion disks.

physics.gen-ph↗

arXiv2021

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

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, $\hbar $, and string, $κ:=\mathit{\ell }_{s}^{3}/6\hbar $, 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.

physics.gen-ph↗

arXiv2021

Broken Scale Invariance, Gravity Mass, and Dark Energy in Modified Einstein Gravity with Two Measure Finsler Like Variables

We study new classes of generic off-diagonal and diagonal cosmological solutions for effective Einstein equations in modified gravity theories, MGTs, with modified dispersion relations, MDRs, encoding possible violations of (local) Lorentz invariance, LIVs. Such MGTs are constructed for Lagrange densities with two non-Riemannian volume forms (two-measure theories, TMTs) and associated bimetric/ biconnection geometric structures. For conventional 2+2 splitting, we can describe such models in Finsler like variables, which is important for elaborating geometric methods of constructing exact and parametric solutions. Such formulations of general relativity, GR, and MGTs are considered for Lorentz manifolds and their (co) tangent bundles, in brief, FTMT. Off-diagonal metrics solving gravitational field equations in FTMTs are determined by generating functions, effective sources and integration constants and characterized by nonholonomic frame torsion effects. Restricting the class of integration functions, we can extract torsionless and diagonal configurations and model emergent cosmological theories with square scalar curvature, $R^2$, when the global Weyl-scale symmetry is broken via nonlinear dynamical interactions with nonholonomic constraints. In the physical Einstein-Finsler frame, the constructions involve (i) nonlinear re-parametrization symmetries of the generating functions and effective sources; (ii) effective potentials for the scalar field with possible two flat regions which allows a unified description of locally anisotropic and/or isotropic early universe inflation related to acceleration cosmology and dark energy; (iii) there are "emergent universes" described by (off-) diagonal solutions for certain nonholonomic phases and parametric cosmological evolution resulting in various inflationary phases; (iv) we can reproduce in two-measure theories massive gravity effects.

physics.gen-ph↗

arXiv2021

Constantin Carathéodory axiomatic approach and Grigory Perelman thermodynamics for geometric flows and cosmological solitonic solutions

We elaborate on statistical thermodynamics models of relativistic geometric flows as generalisations of G. Perelman and R. Hamilton theory centred around C. Carathéodory axiomatic approach to thermodynamics with Pfaffian differential equations. The anholonomic frame deformation method, AFDM, for constructing generic off--diagonal and locally anisotropic cosmological solitonic solutions in the theory of relativistic geometric flows and general relativity is developed. We conclude that such solutions can not be described in terms of the Hawking--Bekenstein thermodynamics for hypersurface, holographic, (anti) de Sitter and similar configurations. The geometric thermodynamic values are defined and computed for nonholonomic Ricci flows, (modified) Einstein equations, and new classes of locally anisotropic cosmological solutions encoding solitonic hierarchies.

physics.gen-ph↗

arXiv2021

Kaluza--Klein gravity & cosmology emerging from G. Perelman's entropy functionals and quantum geometric information flows

We elaborate on quantum geometric information flows, QGIFs, and emergent (modified) Einstein-Maxwell and Kaluza-Klein, KK, theories formulated in Lagrange-Hamilton and general covariant variables. There are considered nonholonomic deformations of Grigory Perelman's F- and W-functionals (originally postulated for Riemannian metrics) for describing relativistic geometric flows, gravity and matter field interactions, and associated statistical thermodynamic systems. We argue that the concept of Perelman W-entropy presents more general and alternative possibilities to characterize geometric flow evolution, GIF, and gravity models than the Bekenstein-Hawking and another area-holographic type entropies. Formulating the theory of QGIFs, a set of fundamental geometric, probability, and quantum concepts, and methods of computation, are reconsidered for curved spacetime and (relativistic) phase spaces. Such generalized metric-affine spaces are modeled as nonholonomic Lorentz manifolds, (co) tangent Lorentz bundles, and associated vector bundles. Using geometric and entropic and thermodynamic values, we define QGIF versions of the von Neumann entropy, relative and conditional entropy, mutual information, etc. There are analyzed certain important inequalities and possible applications of G. Perelman and related entanglement and Rényi entropies to theories of KK QGIFs and emergent gravitational and electromagnetic interactions. New classes of exact cosmological solutions for GIFs and respective quasiperiodic evolution scenarios are elaborated. We show how classical and quantum thermodynamic values can be computed for cosmological quasiperiodic solutions and speculate how such constructions can be used for explaining structure formation in dark energy and dark matter physics.

physics.gen-ph↗