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Sergiu Vacaru

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Dr Sergiu Vacaru has almost 40 years of research (including 5 years of university teaching) experience on mathematical particle physics, gravity and cosmology, and geometric methods in physics, with more than 140 peer-reviewed articles and 190 scientific works (390 titles including 8 monographs and university textbooks and lecture notes, preprints, scientific talks etc.). He received the equivalents of MS and PhD degrees and Research Professor title, CS1, in the former USSR and Romania: at Tomsk Polytechnic University and Moscow State University "M. Lomonosov" in Russia

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Papers by Sergiu Vacaru

Fixed-Point Behaviour

Concise Encyclopedia of Supersymmetry, 2004

Gauge and Einstein Gravity from Non-Abelian Gauge Models on

Following the formalism of enveloping algebras and star product calculus we formulate and analyze... more Following the formalism of enveloping algebras and star product calculus we formulate and analyze a model of gauge gravity on noncommutative spaces and examine the conditions of its equivalence to general relativity. The corresponding Seiber-Witten maps are established which allow the definition of respective dynamics for a finite number of gravitational gauge field components on noncommutative spaces.

$Research paper thumbnail of Dark Energy and Dark Matter Configurations for Wormholes And Solitionic Hierarchies of Nonmetric Ricci Flows and $F(R,T,Q,T_{M})$ Gravity$

Dark Energy and Dark Matter Configurations for Wormholes And Solitionic Hierarchies of Nonmetric Ricci Flows and $F(R,T,Q,T_{M})$ Gravity

Eur. Phys. J. C , 2024

We extend the anholonomic frame and connection deformation method, AFCDM, for constructing exact ... more 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.

Quasi-stationary solutions in gravity theories with modified dispersion relations and Finsler–Lagrange–Hamilton Geometry

European Physical Journal Plus, Jan 28, 2020

Modified gravity theories, MGTs, with modified (nonlinear) dispersion relations, MDRs, encode via... more Modified gravity theories, MGTs, with modified (nonlinear) dispersion relations, MDRs, encode via indicator functionals possible modifications and effects of quantum gravity; in string/brane, noncommutative and/or nonassociative gravity theories etc. MDRs can be with global and/or local Lorentz invariance violations, LIVs, determined by quantum fluctuations, random, kinetic, statistical and/or thermodynamical processes etc. Such MGTs with MDRs and corresponding models of locally anisotropic spacetime and curved phase spaces can be geometrized in an axiomatic form for theories constructed on (co) tangent bundles with base spacetime Lorentz manifolds. In certain canonical nonholonomic variables, the geometric/physical objects are defined equivalently as in generalized Einstein-Finsler and/or Lagrange-Hamilton spaces. In such Finsler like MGTs, the coefficients of metrics and connections depend both on local Lorentz spacetime coordinates and, additionally, on (co) fiber velocity and/or momentum type variables. The main goal of this work is to elaborate on a nonholonomic diadic "shell by shell" formulation of MGTs with MDRs, with a conventional (2+2)+(2+2) splitting of total phase space dimensions, when the (dual) modified Einstein-Hamilton equations can be decoupled in general forms. We show how this geometric formalism allows us to construct various classes of exact and parametric solutions determined by generating and integration functions and effective sources depending, in principle, on all phase space coordinates. There are derived certain most general and important formulas for nonlinear quadratic elements and studied the main geometric and physical properties of quasi-stationary generic off-diagonal and diagonalizable phase spaces. This work provides a self-consistent geometric and analytic method for constructing in our further partner papers different types of black hole solutions for theories with MDRs and LIVs and elaborating various applications in modern cosmology and astrophysics.

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

arXiv (Cornell University), May 30, 2023

We extend to a theory of nonassociative geometric flows a string-inspired model of nonassociative... more 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.

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

arXiv (Cornell University), Jul 9, 2019

We elaborate on quantum geometric information flows, QGIFs, and emergent (modified) Einstein-Maxw... more 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. The geometric and classical and quantum thermodynamics methods allow us to understand and describe important classical and quantum physical properties of more general classes of exact solutions in modified gravity and geometric flow theories. 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 modelled 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.

Nonassociative Ricci Flows, Star Product and R‐flux Deformed Black Holes, and Swampland Conjectures

by Sergiu Vacaru and El\c{s}en Veli Veliev

Fortschritte der Physik, 2023

A theory of nonassociative geometric flows is formulated as an extension of a string‐inspired mod... more A theory of nonassociative geometric flows is formulated as an extension of a string‐inspired model of nonassociative gravity determined by star product. 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. 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 are developed and applied. There are provided explicit examples of solutions modeling geometric and statistical thermodynamic evolution on a temperature‐like parameter of modified black hole configurations encoding nonassociative star‐product and R‐flux deformation data. F...

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

arXiv (Cornell University), Jun 28, 2019

We investigate classical and quantum geometric information flow theories (GIFs and QGIFs) when th... more We investigate classical and quantum geometric information flow theories (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. The term NES encodes models when the fundamental physical equations are subjected to nonholonomic (equivalently, non-integrable, anholonomic) constraints. There are used canonical geometric variables that allow a general decoupling and integration of systems of nonlinear partial differential equations describing GIFs and QGIFs and Ricci soliton type configurations. Our approach is different from the constructions elaborated for special classes of solutions characterized by area-hypersurface entropy, related holographic, and dual gauge-gravity models involving generalizations of the Bekenstein-Hawking entropy. We formulate the theory of QGIFs which in certain quasi-classical limits encodes GIFs and models with flow evolution of NES. There are computed respectively the von Neumann, relative and conditional entropy; mutual information, 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 thermodynamic values and extensions to QGIF models can be computed for various new classes of exact solutions which can not be described following the Bekenstein-Hawking approach.

Correction: Dynamical equations and Lagrange–Ricci flow evolution on prolongation Lie algebroids

Canadian Journal of Physics, 2019

1 Decoupling of EYMH Equations, Off-Diagonal

This paper is concerned with giving the proof that there is a general decoupling property of vacu... more This paper is concerned with giving the proof that there is a general decoupling property of vacuum and nonvacuum gravitational field equations in Einstein gravity and f (R, T)-modifications. The constructions are possible in terms of geometric and physical objects adapted to certain nonholonomic 2+2 splitting with local fibred structure. This allows us to generate exact and/or parametric depending solutions with generic off-diagonal metrics and generalized, or Levi-Civita, connections. Different classes of modified spacetimes are determined by corresponding generating and integration functions depending, in general, on all space and time coordinates and may possess, or not, Killing symmetries. The initial data sets for the Cauchy problem and their global properties are analyzed. There are formulated the criteria of evolution with spacetime splitting and decoupling of fundamental field equations. Examples of exact solutions defining ellipsoid deformations of black hole metrics and solitonic configurations are provided. 6 There is not summation on repeating "low" indices a in formulas (9) but such a summation is considered for crossing "up-low" indices i and a in (8)). We shall underline a function if it positively depends on y 4 but not on y 3 and write, for instance, n i (x k , y 4).

Quantum geometric information flows and emergent gravity

We investigate classical and quantum geometric information flow theories (respectively, GIFs and ... more 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. There are defined canonical (nonholonomic, i.e. with non-integrable distributions) geometric variables which allow a general decoupling and integration of nonlinear systems of equations describing GIFs and QGIFs and (for self-similar geometric flows) Ricci soliton type configurations. Our approach is more general and different from the ideas and methods used for special classes of solutions with the area–hypersurface entropy, and related holographic and dual gauge–gravity models, involving the concepts and generalizations of the Bekenstein–Hawking entropy and black hole thermodynamics. Formulating the theory of QGIFs and GIFs (in particular, encoding models with flow evolution of NES), a set of fundamental geometric, proba...

Nonassociative black holes in R-flux deformed phase spaces and relativistic models of Perelman thermodynamics

Journal of High Energy Physics

This paper explores new classes of black hole (BH) solutions in nonassociative and noncommutative... more This paper explores new classes of black hole (BH) solutions in nonassociative and noncommutative gravity, focusing on features that generalize to higher dimensions. The theories we study are modelled on (co) tangent Lorentz bundles with a star product structure determined by R-flux deformations in string theory. For the nonassociative vacuum Einstein equations we consider both real and complex effective sources. In order to analyze the nonassociative vacuum Einstein equations we develop the anholonomic frame and connection deformation methods, which allows one to decoupled and solve these equations. The metric coefficients can depend on both space-time coordinates and energy-momentum. By imposing conditions on the integration functions and effective sources we find physically important, exact solutions: (1) 6-d Tangherlini BHs, which are star product and R-flux distorted to 8-d black ellipsoids (BEs) and BHs; (2) nonassocitative space-time and co-fiber space double BH and/or BE con...

Fermionic Center

Concise Encyclopedia of Supersymmetry, 2004

Finsler Superspace

Concise Encyclopedia of Supersymmetry, 2004

Fock Space and Infinite Dimensional Superanalysis

Concise Encyclopedia of Supersymmetry, 2004

Entropy functionals and thermodynamics of relativistic geometric flows, stationary quasi-periodic Ricci solitons, and gravity

Annals of Physics, 2020

We investigate gravity models emerging from nonholonomic (subjected to non-integrable constraints... more We investigate gravity models emerging from nonholonomic (subjected to non-integrable constraints) Ricci flows. Considering generalizations of G. Perelman's entropy functionals, relativistic geometric flow equations, nonholonomic Ricci soliton and equivalent (modified) Einstein equations are derived. There are studied nonholonomic configurations which allow explicit modeling of entropic scenarios for gravity and dark matter (in the E. Verlinde approach and/or other variants). It is shown that using the anholonomic frame deformation method, the systems of nonlinear partial differential equations for geometric flow evolution of nonlinear stationary gravitations systems can be decoupled and integrated in general forms. In this and a series of partner works, we elaborate on stationary models of emergent gravity with quasi-periodic gravitational, matter fields and dark energy/matter structure. Such configurations cannot be described thermodynamically using the concept of Bekenstein-Hawking entropy if area-entropy, holographic or duality relations are not involved. Nevertheless, generalizing G. Perelman statistic thermodynamic approach to models of relativistic Ricci flows and nonholonomic solitons, we can compute respective thermodynamic variables for all types of gravitational and matter field configurations and their geometric evolution. Nonholonomic deformations of the F-and W-entropy considered and relativistic thermodynamic models are studied in more general cases when physically important solutions with quasi-periodic and pattern forming structure are found in modified gravity theories (MGT) and general relativity (GR).

Locally anisotropic cosmological systems in modified two measure and massive gravity theories

The Fourteenth Marcel Grossmann Meeting, 2017

We outline a geometric method of constructing generic off-diagonal and diagonal cosmological solu... more We outline a geometric method of constructing generic off-diagonal and diagonal cosmological solutions of effective Einstein equations modeling modified gravity theories with two non-Riemannian volume forms and associated bimetric and/or biconnection geometric structures. Such solutions are determined by generating functions, effective sources and integration constants and characterized by nonholonomic frame torsion effects. In the physical Einstein 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 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 and 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.

Off-diagonal wormhole and black hole deformations and dark energy in two measure/bi-metric modified gravity theories

The Fourteenth Marcel Grossmann Meeting, 2017

We find general parameterizations for generic off-diagonal spacetime metrics and matter sources i... more We find general parameterizations for generic off-diagonal spacetime metrics and matter sources in general relativity (GR) and two measure/bi-metric modified gravity theories, MGTs, when the field equations decouple with respect to nonholonomic frames of reference. This allows us to construct various classes of exact solutions when the coefficients of the fundamental geometric/physical objects depend on all spacetime coordinates via corresponding classes of generating and integration functions and/or constants. Such (modified) spacetimes display Killing and non-Killing symmetries, describe nonlinear vacuum configurations and effective polarizations of cosmological and interaction constants. Certain examples of exact locally anisotropic wormhole and generic off-diagonal cosmological solutions are analysed for MGTs of massive and/or modified f(R,T) gravity, two measure theory etc. We conclude that considering generic off-diagonal nonlinear parametric interactions in GR it is possible to mimic various effects in massive and/or modified gravity, or to distinguish certain classes of generic modified gravity solutions which cannot be encoded in GR.

Kaluza–Klein gravity and cosmology emerging from G. Perelman’s entropy functionals and quantum geometric information flows

The European Physical Journal Plus, 2021

We elaborate on quantum geometric information flows, QGIFs, and emergent (modified) Einstein-Maxw... more 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 modelled 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.

1 Cosmological Solutions in Biconnection and Bimetric Gravity Theories

Fixed-Point Behaviour

Concise Encyclopedia of Supersymmetry, 2004

Gauge and Einstein Gravity from Non-Abelian Gauge Models on

Following the formalism of enveloping algebras and star product calculus we formulate and analyze... more Following the formalism of enveloping algebras and star product calculus we formulate and analyze a model of gauge gravity on noncommutative spaces and examine the conditions of its equivalence to general relativity. The corresponding Seiber-Witten maps are established which allow the definition of respective dynamics for a finite number of gravitational gauge field components on noncommutative spaces.

$Research paper thumbnail of Dark Energy and Dark Matter Configurations for Wormholes And Solitionic Hierarchies of Nonmetric Ricci Flows and $F(R,T,Q,T_{M})$ Gravity$

Dark Energy and Dark Matter Configurations for Wormholes And Solitionic Hierarchies of Nonmetric Ricci Flows and $F(R,T,Q,T_{M})$ Gravity

Eur. Phys. J. C , 2024

We extend the anholonomic frame and connection deformation method, AFCDM, for constructing exact ... more 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.

Quasi-stationary solutions in gravity theories with modified dispersion relations and Finsler–Lagrange–Hamilton Geometry

European Physical Journal Plus, Jan 28, 2020

Modified gravity theories, MGTs, with modified (nonlinear) dispersion relations, MDRs, encode via... more Modified gravity theories, MGTs, with modified (nonlinear) dispersion relations, MDRs, encode via indicator functionals possible modifications and effects of quantum gravity; in string/brane, noncommutative and/or nonassociative gravity theories etc. MDRs can be with global and/or local Lorentz invariance violations, LIVs, determined by quantum fluctuations, random, kinetic, statistical and/or thermodynamical processes etc. Such MGTs with MDRs and corresponding models of locally anisotropic spacetime and curved phase spaces can be geometrized in an axiomatic form for theories constructed on (co) tangent bundles with base spacetime Lorentz manifolds. In certain canonical nonholonomic variables, the geometric/physical objects are defined equivalently as in generalized Einstein-Finsler and/or Lagrange-Hamilton spaces. In such Finsler like MGTs, the coefficients of metrics and connections depend both on local Lorentz spacetime coordinates and, additionally, on (co) fiber velocity and/or momentum type variables. The main goal of this work is to elaborate on a nonholonomic diadic "shell by shell" formulation of MGTs with MDRs, with a conventional (2+2)+(2+2) splitting of total phase space dimensions, when the (dual) modified Einstein-Hamilton equations can be decoupled in general forms. We show how this geometric formalism allows us to construct various classes of exact and parametric solutions determined by generating and integration functions and effective sources depending, in principle, on all phase space coordinates. There are derived certain most general and important formulas for nonlinear quadratic elements and studied the main geometric and physical properties of quasi-stationary generic off-diagonal and diagonalizable phase spaces. This work provides a self-consistent geometric and analytic method for constructing in our further partner papers different types of black hole solutions for theories with MDRs and LIVs and elaborating various applications in modern cosmology and astrophysics.

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

arXiv (Cornell University), May 30, 2023

We extend to a theory of nonassociative geometric flows a string-inspired model of nonassociative... more 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.

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

arXiv (Cornell University), Jul 9, 2019

We elaborate on quantum geometric information flows, QGIFs, and emergent (modified) Einstein-Maxw... more 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. The geometric and classical and quantum thermodynamics methods allow us to understand and describe important classical and quantum physical properties of more general classes of exact solutions in modified gravity and geometric flow theories. 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 modelled 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.

Nonassociative Ricci Flows, Star Product and R‐flux Deformed Black Holes, and Swampland Conjectures

by Sergiu Vacaru and El\c{s}en Veli Veliev

Fortschritte der Physik, 2023

A theory of nonassociative geometric flows is formulated as an extension of a string‐inspired mod... more A theory of nonassociative geometric flows is formulated as an extension of a string‐inspired model of nonassociative gravity determined by star product. 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. 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 are developed and applied. There are provided explicit examples of solutions modeling geometric and statistical thermodynamic evolution on a temperature‐like parameter of modified black hole configurations encoding nonassociative star‐product and R‐flux deformation data. F...

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

arXiv (Cornell University), Jun 28, 2019

We investigate classical and quantum geometric information flow theories (GIFs and QGIFs) when th... more We investigate classical and quantum geometric information flow theories (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. The term NES encodes models when the fundamental physical equations are subjected to nonholonomic (equivalently, non-integrable, anholonomic) constraints. There are used canonical geometric variables that allow a general decoupling and integration of systems of nonlinear partial differential equations describing GIFs and QGIFs and Ricci soliton type configurations. Our approach is different from the constructions elaborated for special classes of solutions characterized by area-hypersurface entropy, related holographic, and dual gauge-gravity models involving generalizations of the Bekenstein-Hawking entropy. We formulate the theory of QGIFs which in certain quasi-classical limits encodes GIFs and models with flow evolution of NES. There are computed respectively the von Neumann, relative and conditional entropy; mutual information, 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 thermodynamic values and extensions to QGIF models can be computed for various new classes of exact solutions which can not be described following the Bekenstein-Hawking approach.

Correction: Dynamical equations and Lagrange–Ricci flow evolution on prolongation Lie algebroids

Canadian Journal of Physics, 2019

1 Decoupling of EYMH Equations, Off-Diagonal

This paper is concerned with giving the proof that there is a general decoupling property of vacu... more This paper is concerned with giving the proof that there is a general decoupling property of vacuum and nonvacuum gravitational field equations in Einstein gravity and f (R, T)-modifications. The constructions are possible in terms of geometric and physical objects adapted to certain nonholonomic 2+2 splitting with local fibred structure. This allows us to generate exact and/or parametric depending solutions with generic off-diagonal metrics and generalized, or Levi-Civita, connections. Different classes of modified spacetimes are determined by corresponding generating and integration functions depending, in general, on all space and time coordinates and may possess, or not, Killing symmetries. The initial data sets for the Cauchy problem and their global properties are analyzed. There are formulated the criteria of evolution with spacetime splitting and decoupling of fundamental field equations. Examples of exact solutions defining ellipsoid deformations of black hole metrics and solitonic configurations are provided. 6 There is not summation on repeating "low" indices a in formulas (9) but such a summation is considered for crossing "up-low" indices i and a in (8)). We shall underline a function if it positively depends on y 4 but not on y 3 and write, for instance, n i (x k , y 4).

Quantum geometric information flows and emergent gravity

We investigate classical and quantum geometric information flow theories (respectively, GIFs and ... more 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. There are defined canonical (nonholonomic, i.e. with non-integrable distributions) geometric variables which allow a general decoupling and integration of nonlinear systems of equations describing GIFs and QGIFs and (for self-similar geometric flows) Ricci soliton type configurations. Our approach is more general and different from the ideas and methods used for special classes of solutions with the area–hypersurface entropy, and related holographic and dual gauge–gravity models, involving the concepts and generalizations of the Bekenstein–Hawking entropy and black hole thermodynamics. Formulating the theory of QGIFs and GIFs (in particular, encoding models with flow evolution of NES), a set of fundamental geometric, proba...

Nonassociative black holes in R-flux deformed phase spaces and relativistic models of Perelman thermodynamics

Journal of High Energy Physics

This paper explores new classes of black hole (BH) solutions in nonassociative and noncommutative... more This paper explores new classes of black hole (BH) solutions in nonassociative and noncommutative gravity, focusing on features that generalize to higher dimensions. The theories we study are modelled on (co) tangent Lorentz bundles with a star product structure determined by R-flux deformations in string theory. For the nonassociative vacuum Einstein equations we consider both real and complex effective sources. In order to analyze the nonassociative vacuum Einstein equations we develop the anholonomic frame and connection deformation methods, which allows one to decoupled and solve these equations. The metric coefficients can depend on both space-time coordinates and energy-momentum. By imposing conditions on the integration functions and effective sources we find physically important, exact solutions: (1) 6-d Tangherlini BHs, which are star product and R-flux distorted to 8-d black ellipsoids (BEs) and BHs; (2) nonassocitative space-time and co-fiber space double BH and/or BE con...

Fermionic Center

Concise Encyclopedia of Supersymmetry, 2004

Finsler Superspace

Concise Encyclopedia of Supersymmetry, 2004

Fock Space and Infinite Dimensional Superanalysis

Concise Encyclopedia of Supersymmetry, 2004

Entropy functionals and thermodynamics of relativistic geometric flows, stationary quasi-periodic Ricci solitons, and gravity

Annals of Physics, 2020

We investigate gravity models emerging from nonholonomic (subjected to non-integrable constraints... more We investigate gravity models emerging from nonholonomic (subjected to non-integrable constraints) Ricci flows. Considering generalizations of G. Perelman's entropy functionals, relativistic geometric flow equations, nonholonomic Ricci soliton and equivalent (modified) Einstein equations are derived. There are studied nonholonomic configurations which allow explicit modeling of entropic scenarios for gravity and dark matter (in the E. Verlinde approach and/or other variants). It is shown that using the anholonomic frame deformation method, the systems of nonlinear partial differential equations for geometric flow evolution of nonlinear stationary gravitations systems can be decoupled and integrated in general forms. In this and a series of partner works, we elaborate on stationary models of emergent gravity with quasi-periodic gravitational, matter fields and dark energy/matter structure. Such configurations cannot be described thermodynamically using the concept of Bekenstein-Hawking entropy if area-entropy, holographic or duality relations are not involved. Nevertheless, generalizing G. Perelman statistic thermodynamic approach to models of relativistic Ricci flows and nonholonomic solitons, we can compute respective thermodynamic variables for all types of gravitational and matter field configurations and their geometric evolution. Nonholonomic deformations of the F-and W-entropy considered and relativistic thermodynamic models are studied in more general cases when physically important solutions with quasi-periodic and pattern forming structure are found in modified gravity theories (MGT) and general relativity (GR).

Locally anisotropic cosmological systems in modified two measure and massive gravity theories

The Fourteenth Marcel Grossmann Meeting, 2017

We outline a geometric method of constructing generic off-diagonal and diagonal cosmological solu... more We outline a geometric method of constructing generic off-diagonal and diagonal cosmological solutions of effective Einstein equations modeling modified gravity theories with two non-Riemannian volume forms and associated bimetric and/or biconnection geometric structures. Such solutions are determined by generating functions, effective sources and integration constants and characterized by nonholonomic frame torsion effects. In the physical Einstein 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 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 and 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.

Off-diagonal wormhole and black hole deformations and dark energy in two measure/bi-metric modified gravity theories

The Fourteenth Marcel Grossmann Meeting, 2017

We find general parameterizations for generic off-diagonal spacetime metrics and matter sources i... more We find general parameterizations for generic off-diagonal spacetime metrics and matter sources in general relativity (GR) and two measure/bi-metric modified gravity theories, MGTs, when the field equations decouple with respect to nonholonomic frames of reference. This allows us to construct various classes of exact solutions when the coefficients of the fundamental geometric/physical objects depend on all spacetime coordinates via corresponding classes of generating and integration functions and/or constants. Such (modified) spacetimes display Killing and non-Killing symmetries, describe nonlinear vacuum configurations and effective polarizations of cosmological and interaction constants. Certain examples of exact locally anisotropic wormhole and generic off-diagonal cosmological solutions are analysed for MGTs of massive and/or modified f(R,T) gravity, two measure theory etc. We conclude that considering generic off-diagonal nonlinear parametric interactions in GR it is possible to mimic various effects in massive and/or modified gravity, or to distinguish certain classes of generic modified gravity solutions which cannot be encoded in GR.

Kaluza–Klein gravity and cosmology emerging from G. Perelman’s entropy functionals and quantum geometric information flows

The European Physical Journal Plus, 2021

We elaborate on quantum geometric information flows, QGIFs, and emergent (modified) Einstein-Maxw... more 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 modelled 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.

1 Cosmological Solutions in Biconnection and Bimetric Gravity Theories