arXiv subjects

Sergiu I. Vacaru

Publications and source records attributed to Sergiu I. Vacaru.

At least 37 records · Page 2Linked to original sources

arXiv2020

Off-diagonal cosmological solutions in emergent gravity theories and Grigory Perelman entropy for geometric flows

We develop an approach to the theory of relativistic geometric flows and emergent gravity defined by entropy functionals and related statistical thermodynamics models. Nonholonomic deformations of G. Perelman's functionals and related entropic values are used for deriving relativistic geometric evolution flow equations. For self-similar configurations, such equations describe generalized Ricci solitons defining modified Einstein equations. We analyze possible connections between relativistic models of nonholonomic Ricci flows and emergent modified gravity theories. We prove that corresponding systems of nonlinear partial differential equations, PDEs, for entropic flows and modified gravity possess certain general decoupling and integration properties. There are constructed new classes of exact and parametric solutions for nonstationary configurations and locally anisotropic cosmological metrics in modified gravity theories and general relativity. Such solutions describe scenarios of nonlinear geometric evolution and gravitational and matter field dynamics with pattern-forming and quasiperiodic structure and various space quasicrystal and deformed spacetime crystal models. We analyze new classes of generic off-diagonal solutions for entropic gravity theories and show how such solutions can be used for explaining structure formation in modern cosmology. Finally, we speculate why the approaches with Perelman-Lyapunov type functionals are more general or complementary to the constructions elaborated using the concept of Bekenstein-Hawking entropy.

physics.gen-ph↗

arXiv2020

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

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 that 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).

physics.gen-ph↗

arXiv2020

Geometric information flows and G. Perelman entropy for relativistic classical and quantum mechanical systems

This work consists an introduction to the classical and quantum information theory of geometric flows of (relativistic) Lagrange--Hamilton mechanical systems. Basic geometric and physical properties of the canonical nonholonomic deformations of G. Perelman entropy functionals and geometric flows evolution equations of classical mechanical systems are described. There are studied projections of such F- and W-functionals on Lorentz spacetime manifolds and three-dimensional spacelike hypersurfaces. These functionals are used for elaborating relativistic thermodynamic models for Lagrange--Hamilton geometric evolution and respective generalized R. Hamilton geometric flow and nonholonomic Ricci flow equations. The concept of nonholonomic W-entropy is developed as a complementary one for the classical Shannon entropy and the quantum von Neumann entropy. There are considered geometric flow generalizations of the approaches based on classical and quantum relative entropy, conditional entropy, mutual information, and related thermodynamic models. Such basic ingredients and topics of quantum geometric flow information theory are elaborated using the formalism of density matrices and measurements with quantum channels for the evolution of quantum mechanical systems.

physics.gen-ph↗

arXiv2020

Classical and quantum geometric information flows and entanglement of relativistic mechanical systems

This article elaborates on entanglement entropy and quantum information theory of geometric flows of (relativistic) Lagrange--Hamilton mechanical systems. A set of basic geometric and quantum mechanics and probability concepts together with methods of computation are developed in general covariant form for curved phase spaces modelled as cotangent Lorentz bundles. The constructions are based on ideas relating the Grigory Perelman's entropy for geometric flows and associated statistical thermodynamic systems to the quantum von Neumann entropy, classical and quantum relative and conditional entropy, mutual information etc. We formulate the concept of the entanglement entropy of quantum geometric information flows and study properties and inequalities for quantum, thermodynamic and geometric entropies characterising such systems.

physics.gen-ph↗

arXiv2020

Quasi-Stationary Solutions in Gravity Theories with Modified Dispersion Relations and Finsler-Lagrange-Hamilton Geometry

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. 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.

physics.gen-ph↗

arXiv2019

Black Holes with MDRs and Bekenstein-Hawking and Perelman Entropies for Finsler-Lagrange-Hamilton Spaces

New geometric and analytic methods for generating exact and parametric solutions in generalized Einstein-Finsler like gravity theories and nonholonomic Ricci soliton models are reviewed and developed. We show how generalizations of the Schwarzschild - (anti) de Sitter metric can be constructed for modified gravity theories with arbitrarily modified dispersion relations, MDRs, and Lorentz invariance violations, LIVs. Such theories can be geometrized on cotangent Lorentz bundles (phase spaces) as models of relativistic Finsler-Lagrange-Hamilton spaces. There are considered two general classes of solutions for gravitational stationary vacuum phase space configurations and nontrivial (effective) matter sources or cosmological constants. Such solutions describe nonholonomic deformations of conventional higher dimension black hole, BH, solutions with general dependence on effective four-dimensional, 4-d, momentum type variables. For the first class, we study physical properties of Tangherlini like BHs in phase spaces with generic dependence on an energy coordinate/ parameter. We investigate also BH configurations on base spacetime and in curved cofiber spaces when the BH mass and the maximal speed of light determine naturally a cofiber horizon. For the second class, the solutions are constructed with Killing symmetry on an energy type coordinate. There are analysed the conditions when generalizations of Beckenstein-Hawking entropy (for solutions with conventional horizons) and/or Grigory Perelman's W-entropy (for more general generic off-diagonal solutions) can be defined for phase space stationary configurations.

physics.gen-ph↗

arXiv2018

Space-Time Quasicrystal Structures and Inflationary and Late Time Evolution Dynamics in Accelerating Cosmology

We construct new classes of cosmological solutions in modified and Einstein gravity theories encoding space-time quasicrystal, STQC, configurations modelled by nonlinear self-organized and pattern forming quasi-periodic structures. Such solutions are defined by generic off-diagonal locally anisotropic and inhomogeneous metrics depending via generating and integration functions on all spacetime coordinates. There are defined nonholonomic variables and conditions for the generating/integration functions and sources for effective descriptions, or approximations, as "quasi" Friedmann-Lamaître-Robertson-Walker (FLRW) metrics. Such (off-) diagonal STQC-FLRW configurations contain memory on nonlinear classical and/or quantum interactions and may describe new acceleration cosmology scenarios. For special time-periodic conditions on nonlinear gravitational and matter field interactions, we can model at cosmological scales certain analogous of time crystal like structures originally postulated by Frank Wilczek in condensed matter physics. We speculate how STQC quasi-FLRW configurations could explain modern cosmology data and provide viable descriptions for the inflation and structure formation in our Universe. Finally, it is discussed systematically and critically how a unified description of inflation with dark energy era can be explained by (modified) cosmological STQC-scenarios.

physics.gen-ph↗

arXiv2018

Dynamical Equations and Lagrange--Ricci Flow Evolution on Prolongation Lie Algebroids

The approach to nonholonomic Ricci flows and geometric evolution of regular Lagrange systems [S. Vacaru: J. Math. Phys. \textbf{49} (2008) 043504 \& Rep. Math. Phys. \textbf{63} (2009) 95] is extended to include geometric mechanics and gravity models on Lie algebroids. We prove that such evolution scenarios of geometric mechanics and analogous gravity can be modelled as gradient flows characterized by generalized Perelman functionals if an equivalent geometrization of Lagrange mechanics [J. Kern, Arch. Math. (Basel) \textbf{25} (1974) 438] is considered. The R. Hamilton equations on Lie algebroids describing Lagrange-Ricci flows are derived. Finally, we show that geometric evolution models on Lie algebroids are described by effective thermodynamical values derived from statistical functionals on prolongation Lie algebroids.

math-ph↗

arXiv2018

Deforming Black Hole and Cosmological Solutions by Quasiperiodic and/or Pattern Forming Structures in Modified and Einstein Gravity

We elaborate on the anholonomic frame deformation method, AFDM, for constructing exact solutions with quasiperiodic structure in modified gravity theories, MGTs, and general relativity, GR. Such solutions are described by generic off-diagonal metrics, nonlinear and linear connections and (effective) matter sources with coefficients depending on all spacetime coordinates via corresponding classes of generation and integration functions and (effective) matter sources. There are studied effective free energy functionals and nonlinear evolution equations for generating off-diagonal quasiperiodic deformations of black hole and/or homogeneous cosmological metrics. The physical data for such functionals are stated by different values of constants and prescribed symmetries for defining quasiperiodic structures at cosmological scales, or astrophysical objects in nontrivial gravitational backgrounds some similar forms as in condensed matter physics. It is shown how quasiperiodic structures determined by general nonlinear, or additive, functionals for generating functions and (effective) sources may transform black hole like configurations into cosmological metrics and inversely. We speculate on possible implications of quasiperiodic solutions in dark energy and dark matter physics. Finally, it is concluded that geometric methods for constructing exact solutions consist an important alternative tool to numerical relativity for investigating nonlinear effects in astrophysics and cosmology.

physics.gen-ph↗

arXiv2018

On axiomatic formulation of gravity and matter field theories with MDRs and Finsler-Lagrange-Hamilton geometry on (co)tangent Lorentz bundles

We develop an axiomatic geometric approach and provide an unconventional review of modified gravity theories, MGTs, with modified dispersion relations, MDRs, encoding Lorentz invariance violations, LIVs, classical and quantum random effects, anisotropies etc. There are studied Lorentz-Finsler like theories elaborated as extensions of general relativity, GR, and quantum gravity, QG, models and constructed on (co) tangent Lorentz bundles, i.e. (curved) phase spaces or locally anisotropic spacetimes. An indicator of MDRs is considered as a functional on various type functions depending on phase space coordinates and physical constants. It determines respective generating functions and fundamental physical objects (generalized metrics, connections and nonholonomic frame structures) for relativistic models of Finsler, Lagrange and/or Hamilton spaces. We show that there are canonical almost symplectic differential forms and adapted (non) linear connections which allow us to formulate equivalent almost Kähler-Lagrange / - Hamilton geometries. This way, it is possible to unify geometrically various classes of (non) commutative MGTs with locally anisotropic gravitational, scalar, non-Abelian gauge field, and Higgs interactions. We elaborate on theories with Lagrangian densities containing massive graviton terms and bi-connection and bi-metric modifications which can be modelled as Finsler-Lagrange-Hamilton geometries. An appendix contains historical remarks on elaborating Finsler MGTs and a summary of author's results in twenty directions of research on (non) commutative/ supersymmetric Finsler geometry and gravity; nonholonomic geometric flows, locally anisotropic superstrings and cosmology, etc.

physics.gen-ph↗

arXiv2017

Anamorphic Quasiperiodic Universes in Modified and Einstein Gravity with Loop Quantum Gravity Corrections

The goal of this work is to elaborate on new geometric methods of constructing exact and parametric quasiperiodic solutions for anamorphic cosmology models in modified gravity theories, MGTs, and general relativity, GR. There exist previously studied generic off-diagonal and diagonalizable cosmological metrics encoding gravitational and matter fields with quasicrystal like structures, QC, and holonomy corrections from loop quantum gravity, LQG. We apply the anholonomic frame deformation method, AFDM, in order to decouple the (modified) gravitational and matter field equations in general form. This allows us to find integral varieties of cosmological solutions determined by generating functions, effective sources, integration functions and constants. The coefficients of metrics and connections for such cosmological configurations depend, in general, on all spacetime coordinates and can be chosen to generate observable (quasi)-periodic/ aperiodic/ fractal / stochastic / (super) cluster / filament / polymer like (continuous, stochastic, fractal and/or discrete structures) in MGTs and/or GR. In this work, we study new classes of solutions for anamorphic cosmology with LQG holonomy corrections. Such solutions are characterized by nonlinear symmetries of generating functions for generic off--diagonal cosmological metrics and generalized connections, with possible nonholonomic constraints to Levi-Civita configurations and diagonalizable metrics depending only on a time like coordinate. We argue that anamorphic quasiperiodic cosmological models integrate the concept of quantum discrete spacetime, with certain gravitational QC-like vacuum and nonvacuum structures. And, that of a contracting universe that homogenizes, isotropizes and flattens without introducing initial conditions or multiverse problems.

gr-qc↗

arXiv2017

On Supersymmetric Geometric Flows and $\mathcal{R}^2$ Inflation From Scale Invariant Supergravity

Models of geometric flows pertaining to $\mathcal{R}^2$ scale invariant (super) gravity theories coupled to conformally invariant matter fields are investigated. Related to this work are supersymmetric scalar manifolds that are isomorphic to the Kählerian spaces $\mathcal{M}_n=SU(1,1+k)/U(1)\times SU(1+k)$ as generalizations of the non-supersymmetric analogs with $SO(1,1+k)/SO(1+k)$ manifolds. For curved superspaces with geometric evolution of physical objects, a complete supersymmetric theory has to be elaborated on nonholonomic (super) manifolds and bundles determined by non-integrable superdistributions with additional constraints on (super) field dynamics and geometric evolution equations. We also consider generalizations of Perelman's functionals using such nonholonomic variables which result in the decoupling of geometric flow equations and Ricci soliton equations with supergravity modifications of the $R^2$ gravity theory. As such, it is possible to construct exact non-homogeneous and locally anisotropic cosmological solutions for various types of (super) gravity theories modelled as modified Ricci soliton configurations. Such solutions are defined by employing the general ansatz encompassing coefficients of generic off-diagonal metrics and generalized connections that depend generically on all spacetime coordinates. We consider nonholonomic constraints resulting in diagonal homogeneous configurations encoding contributions from possible nonlinear parametric geometric evolution scenarios, off-diagonal interactions and anisotropic polarization/ modification of physical constants. We also analyze the conditions under which such modified mimetic type theories and solutions reproduce the Starobinsky inflationary models in the double scalar approach.

hep-th↗

arXiv2017

Cosmological Attractors and Anisotropies in Two Measure Theories, Effective EYMH systems, and Off--Diagonal Inflation Models

Applying the anholonomic frame deformation method, we construct various classes of cosmological solutions for effective Einstein -- Yang-Mills -- Higgs, and two measure theories. The types of models considered are Freedman-Lemaître-Robertson-Walker, Bianchi, Kasner and models with attractor configurations. The various regimes pertaining to plateau--type inflation, quadratic inflation, Starobinsky type and Higgs type inflation are presented.

physics.gen-ph↗

arXiv2017

On Relativistic Generalization of Perelman's W-entropy and Statistical Thermodynamic Description of Gravitational Fields

Using double 2+2 and 3+1 nonholonomic fibrations on Lorentz manifolds, we extend the concept of W-entropy for gravitational fields in the general relativity, GR, theory. Such F- and W-functionals were introduced in the Ricci flow theory of three dimensional, 3-d, Riemannian metrics by G. Perelman, arXiv: math.DG/0211159. Nonrelativistic 3-d Ricci flows are characterized by associated statistical thermodynamical values determined by W--entropy. Generalizations for geometric flows of 4-d pseudo-Riemannian metrics are considered for models with local thermodynamical equilibrium and separation of dissipative and non-dissipative processes in relativistic hydrodynamics. The approach is elaborated in the framework of classical filed theories (relativistic continuum and hydrodynamic models) without an underlying kinetic description which will be elaborated in other works. The 3+1 splitting allows us to provide a general relativistic definition of gravitational entropy in the Lyapunov-Perelman sense. It increases monotonically as structure forms in the Universe. We can formulate a thermodynamic description of exact solutions in GR depending, in general, on all spacetime coordinates. A corresponding 2+2 splitting with nonholonomic deformation of linear connection and frame structures is necessary for generating in very general form various classes of exact solutions of the Einstein and general relativistic geometric flow equations. Finally, we speculate on physical macrostates and microstate interpretations of the W-entropy in GR, geometric flow theories and possible connections to string theory (a second unsolved problem also contained in Perelman's works) in the Polyakov's approach.

gr-qc↗

arXiv2017

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

Heterotic supergravity with (1+3)--dimensional domain wall configurations and (warped) internal, six dimensional, almost-Kähler manifolds $\ ^6\mathbf{X}$ are studied. Considering ten dimensional spacetimes with nonholonomic distributions and conventional double fibrations, 2+2+...=2+2+3+3, and associated $SU(3)$ structures on internal space, we generalize for real, internal, almost symplectic gravitational structures the constructions with gravitational and gauge instantons of tanh-kink type. They include the first $α^{\prime}$ corrections to the heterotic supergravity action, parameterized in a form to imply nonholonomic deformations of the Yang-Mills sector and corresponding Bianchi identities. We show how it is possible to construct a variety of solutions depending on the type of nonholonomic distributions and deformations of 'prime' instanton configurations characterized by two real supercharges. This corresponds to $\mathcal{N}=1/2$ supersymmetric, nonholonomic manifolds from the four dimensional point of view. Our method provides a unified description of embedding nonholonomically deformed tanh-kink-type instantons into half-BPS solutions of heterotic supergravity. This allows us to elaborate new geometric methods of constructing exact solutions of motion equations, with first order $α^{\prime}$ corrections to the heterotic supergravity. Such a formalism is applied for general and/or warped almost-Kähler configurations, which allows us to generate nontrivial (1+3)-d domain walls and black hole deformations determined by quasiperiodic internal space structures. This formalism is utilized in our associated publication [EPJC 77 (2017) 17, arXiv: 1608.01980] in order to construct and study generic off-diagonal nonholonomic deformations of the Kerr metric, encoding contributions from heterotic supergravity.

physics.gen-ph↗

arXiv2016

Off-Diagonal Deformations of Kerr Metrics and Black Ellipsoids in Heterotic Supergravity

Geometric methods for constructing exact solutions of motion equations with first order $α^{\prime}$ corrections to the heterotic supergravity action implying a non-trivial Yang-Mills sector and six dimensional, 6-d, almost-Kähler internal spaces are studied. In 10-d spacetimes, general parametrizations for generic off-diagonal metrics, nonlinear and linear connections and matter sources, when the equations of motion decouple in very general forms are considered. This allows us to construct a variety of exact solutions when the coefficients of fundamental geometric/physical objects depend on all higher dimensional spacetime coordinates via corresponding classes of generating and integration functions, generalized effective sources and integration constants. Such generalized solutions are determined by generic off-diagonal metrics and nonlinear and/or linear connections. In particular, as configurations which are warped/compactified to lower dimensions and for Levi-Civita connections. The corresponding metrics can have (non) Killing and/or Lie algebra symmetries and/or describe (1+2)-d and/or (1+3)-d domain wall configurations, with possible warping nearly almost-Kähler manifolds, with gravitational and gauge instantons for nonlinear vacuum configurations and effective polarizations of cosmological and interaction constants encoding string gravity effects. A series of examples of exact solutions describing generic off-diagonal supergravity modifications to black hole/ ellipsoid and solitonic configurations are provided and analyzed. We prove that it is possible to reproduce the Kerr and other type black solutions in general relativity (with certain types of string corrections) in 4-d and to generalize the solutions to non-vacuum configurations in (super) gravity/ string theories.

hep-th↗

arXiv2016

Nonholonomic Jet Deformations and Exact Solutions for Modified Ricci Soliton and Einstein Equations

Let $\mathbf{g}$ be a pseudo--Riemanian metric of arbitrary signature on a manifold $\mathbf{V}$ with conventional $n+n$ dimensional splitting, $\ n\geq 2,$ determined by a nonholonomic (non--integrable) distribution $\mathcal{N}$ defining a generalized (nonlinear) connection and associated nonholonomic frame structures. We shall work with a correspondingly adapted linear metric compatible connection $\hat{\mathbf{D}}$ and its nonzero torsion $\hat{\mathcal{T}}$, both completely determined by $\mathbf{g}$. Our first goal is to prove that there are certain generalized frame and/or jet transforms and prolongations with $(\mathbf{g},\mathbf{V})\rightarrow (\hat{\mathbf{g}},\hat{\mathbf{V}})$ into explicit classes of solutions of some generalized Einstein equations $\hat{\mathbf{R}}\mathit{ic}=Λ\hat{\mathbf{g}}$, $Λ=const$, encoding various types of nonholonomic) Ricci soliton configurations and/or jet variables and symmetries. The second goal is to solve additional constraint equations for zero torsion, $\hat{\mathcal{T}}=0$, on generalized solutions constructed in explicit forms with jet variables and extract Levi-Civita configurations. This allows us to find generic off-diagonal exact solutions depending on all space time coordinates on $\mathbf{V}$ via generating and integration functions and various classes of constant jet parameters and associated symmetries. We shall study (third goal) how such generalized metrics and connections can be related by so-called "half-conformal" and/ or jet deformations of certain sub-classes of solutions with one, or two, Killing symmetries. Finally, there are considered some examples when exact solutions are constructed as nonholonomic jet prolongations of the Kerr metrics, with possible Ricci soliton deformations, and characterized by nonholonomic jet structures and generalized connections.

math-ph↗

arXiv2016

Geometric Flows and Perelman's Thermodynamics for Black Ellipsoids in $R^2$ and Einstein Gravity Theories

We study geometric relativistic flow and Ricci soliton equations which (for respective nonholonomic constraints and self-similarity conditions) are equivalent to the gravitational field equations of $R^2$ gravity and/or to the Einstein equations with scalar field in general relativity, GR. Perelman's functionals are generalized for modified gravity theories, MGTs, which allows to formulate an analogous statistical thermodynamics for geometric flows and Ricci solitons. There are constructed and analyzed generic off-diagonal black ellipsoid, black hole and solitonic exact solutions in MGTs and GR encoding geometric flow evolution scenarios and nonlinear parametric interactions. Such new classes of solutions in MGTs can be with polarized and/or running constants, nonholonomically deformed horizons and/or imbedded self-consistently into solitonic backgrounds. They exist also in GR as generic off-diagonal vacuum configurations with effective cosmological constant and/or mimicking effective scalar field interactions. Finally, we compute Perelman's energy and entropy for black ellipsoids and evolution solitons in $R^2$ gravity.

gr-qc↗