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Sergiu I. Vacaru

Publications and source records attributed to Sergiu I. Vacaru.

At least 163 records · Page 9Linked to original sources
arXiv2000

Locally Anisotropic Kinetic Processes and Thermodynamics in Curved Spaces

The kinetic theory is formulated with respect to anholonomic frames of reference on curved spacetimes. By using the concept of nonlinear connection we develop an approach to modelling locally anisotropic kinetic processes and, in corresponding limits, the relativistic non-equilibrium thermodynamics with local anisotropy. This lead to a unified formulation of the kinetic equations on (pseudo) Riemannian spaces and in various higher dimensional models of Kaluza-Klein type and/or generalized Lagrange and Finsler spaces. The transition rate considered for the locally anisotropic transport equations is related to the differential cross section and spacetime parameters of anisotropy. The equations of states for pressure and energy in locally anisotropic thermodynamics are derived. The obtained general expressions for heat conductivity, shear and volume viscosity coefficients are applied to determine the transport coefficients of cosmic fluids in spacetimes with generic local anisotropy. We emphasize that such locally anisotropic structures are induced also in general relativity if we are modelling physical processes with respect to frames with mixed sets of holonomic and anholonomic basis vectors which naturally admits an associated nonlinear connection structure.

gr-qc↗
arXiv2000

Gauge and Einstein Gravity from Non-Abelian Gauge Models on Noncommutative Spaces

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 Seiberg-Witten maps are established which allow the definition of respective dynamics for a finite number of gravitational gauge field components on noncommutative spaces.

hep-th↗
arXiv2000

Locally Anisotropic Structures and Nonlinear Connections in Einstein and Gauge Gravity

We analyze local anisotropies induced by anholonomic frames and associated nonlinear connections in general relativity and extensions to affine Poincare and de Sitter gauge gravity and different types of Kaluza-Klein theories. We construct some new classes of cosmological solutions of gravitational field equations describing Friedmann-Robertson-Walker like universes with rotation (ellongated and flattened) ellipsoidal or torus symmetry.

gr-qc↗
arXiv2000

Nonlinear Connections and Nearly Autoparallel Maps in General Relativity

We apply the method of moving anholonomic frames, with associated nonlinear connections, in (pseudo) Riemannian spaces and examine the conditions when various types of locally anisotropic (la) structures (Lagrange, Finsler like and more general ones) could be modeled in general relativity. New classes of solutions of the Einstein equations with generic local anisotropy are constructed. We formulate the theory of nearly autoparallel (na) maps and introduce the tensorial na-integration as the inverse operation to both covariant derivation and deformation of connections by na-maps. The problem of redefinition of the Einstein gravity theory on na-backgrounds, provided with a set of na-map invariant conditions and local conservation laws, is analyzed. There are illustrated some examples of generation of vacuum Einstein fields by Finsler like metrics and chains of na-maps.

gr-qc↗
arXiv2000

Anholonomic Soliton-Dilaton and Black Hole Solutions in General Relativity

A new method of construction of integral varieties of Einstein equations in three dimensional (3D) and 4D gravity is presented whereby, under corresponding redefinition of physical values with respect to anholonomic frames of reference with associated nonlinear connections, the structure of gravity field equations is substantially simplified. It is shown that there are 4D solutions of Einstein equations which are constructed as nonlinear superpositions of soliton solutions of 2D (pseudo) Euclidean sine-Gordon equations (or of Lorentzian black holes in Jackiw-Teitelboim dilaton gravity). The Belinski-Zakharov-Meison solitons for vacuum gravitational field equations are generalized to various cases of two and three coordinate dependencies, local anisotropy and matter sources. The general framework of this study is based on investigation of anholonomic soliton-dilaton black hole structures in general relativity. We prove that there are possible static and dynamical black hole, black torus and disk/cylinder like solutions (of non-vacuum gravitational field equations) with horizons being parametrized by hypersurface equations of rotation ellipsoid, torus, cylinder and another type configurations. Solutions describing locally anisotropic variants of the Schwarzschild-- Kerr (black hole), Weyl (cylindrical symmetry) and Neugebauer--Meinel (disk) solutions with anisotropic variable masses, distributions of matter and interaction constants are shown to be contained in Einstein's gravity. It is demonstrated in which manner locally anisotropic multi-soliton-- dilaton-black hole type solutions can be generated.

gr-qc↗
arXiv2000

Locally Anisotropic Black Holes in Einstein Gravity

By applying the method of moving frames modelling one and two dimensional local anisotropies we construct new solutions of Einstein equations on pseudo-Riemannian spacetimes. The first class of solutions describes non-trivial deformations of static spherically symmetric black holes to locally anisotropic ones which have elliptic (in three dimensions) and ellipsoidal, toroidal and elliptic and another forms of cylinder symmetries (in four dimensions). The second class consists from black holes with oscillating elliptic horizons.

gr-qc↗
arXiv2000

Stochastic Processes and Thermodynamics on Curved Spaces

Our approach views the thermodynamics and kinetics in general relativity and extended gravitational theories (with generic local anisotropy) from the perspective of the theory of stochastic differential equations on curved spaces. Nonequilibrium and irreversible processes in black hole thermodynamics are considered. The paper summarizes the author's contribution to Journees Relativistes 99 (12--17 September 1999), Weimar, Germany.

gr-qc↗
arXiv1999

Thermodynamic Geometry and Locally Anisotropic Black Holes

Thermodynamic properties of locally anisotropic (2+1)-black holes are studied by applying geometric methods. We consider a new class of black holes with a constant in time elliptical event horizon which is imbedded in a generalized Finsler like spacetime geometry induced from Einstein gravity. The corresponding thermodymanic systems are three dimensional with entropy S being a hypersurface function on mass M, anisotropy angle $θ$ and eccentricity of elliptic deformations $ε$. Two-dimensional curved thermodynamic geometries for locally anistropic deformed black holes are constructed after integration on anisotropic parameter $θ$. Two approaches, the first one based on two-dimensional hypersurface parametric geometry and the second one developed in a Ruppeiner-Mrugala-Janyszek fashion, are analyzed. The thermodynamic curvatures are computed and the critical points of curvature vanishing are defined.

gr-qc↗
arXiv1998

Gauge Gravity and Conservation Laws in Higher Order Anisotropic Spaces

We propose an approach to the theory of higher order anisotropic field interactions and curved spaces (in brief, ha-field, ha-interactions and ha-spaces). The concept of ha-space generalises various types of Lagrange and Finsler spaces and higher dimension (Kaluza-Klein) spaces. This work consists from two parts. In the first we outline the theory of Yang-Mills ha-fields and two gauge models of higher order anisotropic gravity are analyzed. The second is devoted to the theory of nearly autoparallel maps (na-maps) of locally anisotropic spaces (la-spaces) and to the problem of formulation of conservation laws for la-field interactions. By defining invariants of na-map transforms we present a systematic classification of la-spaces.

hep-th↗
arXiv1998

Spinors and Field Interactions in Higher Order Anisotropic Spaces

We formulate the theory of field interactions with higher order anisotropy. The concepts of higher order anisotropic space and locally anisotropic space (in brief, ha-space and la-space) are introduced as general ones for various types of higher order extensions of Lagrange and Finsler geometry and higher dimension (Kaluza-Klein type) spaces. The spinors on ha-spaces are defined in the framework of the geometry of Clifford bundles provided with compatible nonlinear and distinguished connections and metric structures (d-connection and d-metric). The spinor differential geometry of ha-spaces is constructed. There are discussed some related issues connected with the physical aspects of higher order anisotropic interactions for gravitational, gauge, spinor, Dirac spinor and Proca fields. Motion equations in higher order generalizations of Finsler spaces, of the mentioned type of fields, are defined by using bundles of linear and affine frames locally adapted to the nonlinear connection structure.

hep-th↗
arXiv1998

Exact Solutions in Locally Anisotropic Gravity and Strings

In this Report we outline some basic results on generalized Finsler--Kaluza--Klein gravity and locally anisotropic strings. There are investigated exact solutions for locally anisotropic Friedmann--Robertson--Walker universes and three dimensional and string black holes with generic anisotropy.

gr-qc↗
arXiv1997

Interactions and Strings in Higher Order Anisotropic and Inhomogeneous Superspaces and Isospaces

The monograph gives a general geometric background of the theory of field interactions, strings and diffusion processes on spaces, superspaces and isospaces with higher order anisotropy and inhomogenity. Our approach proceeds by developing the concept of higher order anisotropic superspace which unify the logical and mathematical aspects of modern Kaluza-Klein theories and generalized Lagrange and Finsler geometry and leads to modelling of physical processes on higher order fiber bundles provided with nonlinear and distingushed connections and metric structures. The view adopted in the monograph is that a general field theory should incorporate all possible anisotropic and stochastic manifestations of classical and quantum interactions and, in consequence, a corresponding modification of basic principles and mathematical methods in formulation of physical theories. This book can be also considered as a pedagogical survey on the mentioned subjects.

physics.gen-ph↗
arXiv1997

Studies on Santilli's Locally Anisotropic and Inhomogeneous Isogeometries: I. Isobundles and Generalized Isofinsler Geometry

We generalize the geometry of Santilli's locally anisotropic and inhomogeneous isospaces to the geometry of vector isobundles provided with nonlinear and distinguished isoconnections and isometric structures. We present, apparently for the first time, the isotopies of Lagrange, Finsler and Kaluza-Klein spaces. We also continue the study of the interior, locally anisotropic and inhomogeneous gravitation by extending the isoriemannian space's constructions and presenting a geometric background for the theory of isofield interactions in generalized isolagrange and isofinsler spaces.

physics.gen-ph↗
arXiv1997

Studies on Santilli's Locally Anisotropic and Inhomogeneous Isogeometries: I. Isobundles and Generalized Isofinsler Gravity

We generalize the geometry of Santilli's locally anisotropic and inhomogeneous isospaces to the geometry of vector isobundles provided with nonlinear and distinguished isoconnections and isometric structures. We present, apparently for the first time, the isotopies of Lagrange, Finsler and Kaluza--Klein spaces. We also continue the study of the interior, locally anisotropic and inhomogeneous gravitation by extending the isoriemannian space's constructions and presenting a geometric background for the theory of isofield interactions in generalized isolagrange and isofinsler spaces.

physics.gen-ph↗
arXiv1996

Field Interactions and Strings in Higher Order Anisotropic Spaces

We present a geometric approach to the field theory with higher order anisotropic interactions. The concepts of higher order space, or locally anisotropic, space (in brief, h-space, or la-space) are introduced as general ones for various types of higher order extensions of Lagrange and Finsler geometry and higher dimension (Kaluza-Klein type) spaces. The spinors on h-spaces are defined in the framework of the geometry of Clifford bundles provided with compatible nonlinear and distinguished connections and metric structures (d-connection and d-metric). There are discussed some related issues connected with the geometric aspects of higher order anisotropc interactions for gravitational, gauge, spinor, Dirac spinor and Proca fields. The nearly autoparallel maps are introduced as maps with deformation of connections extending the class of geodesic and conformal transforms. We propose two variants of solution of the problem of definition of conservation laws on h-spaces. A general background of the theory of field interactions and strings in spaces with higher order anisotropy is fromulated. The conditions for consistent propagation of closed strings in higher order anisotropic background spaces are analyzed. The connection between the conformal invariance, the vanishing of the renormalization group beta-function of the generalized sigma-model and field equations of higher order anisotropic gravity are studied in detail.

hep-th↗
arXiv1996

Superstrings in Higher Order Extensions of Finsler Superspaces

The work proposes a geometric background of the theory of field interactions and strings in spaces with higher order anisotropy. Our approach proceeds by developing the concept of higher order anisotropic superspace which unifies the logical and mathematical aspects of modern Kaluza-Klein theories and generalized Lagrange and Finsler geometry and leads to modelling of physical processes on higher order fiber bundles provided with nonlinear and distingushed connections and metric structures. The view adopted is that a general field theory should incorporate all possible anisotropic and stochastic manifestations of classical and quantum interactions and, in consequence, a corresponding modification of basic principles and mathematical methods in formulation of physical theories. The presentation is divided into two parts. The first five sections cover the higher order anisotropic superspaces. We focus on the geometry of distinguished by nonlinear connection vector superbundles, consider different supersymmetric extensions of Finsler and Lagrange spaces and analyze the structure of basic geometric objects on such superspaces. The remaining five sections are devoted to the theory of higher order anisotropic superstrings. In the framework of supersymmetric nonlinear sigma models in Finser extended backgrounds we prove that the low-energy dynamics of such strings contains motion equations for locally anisotropic field interactions.

hep-th↗
arXiv1996

Spinors, Nonlinear Connections, and Nearly Autoparallel Maps of Generalized Finsler Spaces

We review the geometric setting of the field theory with locally anisotropic interactions. The concept of locally anisotropic space is introduced as a general one for various type of extensions of Lagrange and Finsler geometry and higher dimension (Kaluza--Klein type) spaces. The problem of definition of spinors on generalized Finsler spaces is solved in the framework of the geometry of Clifford bundles provided with compatible nonlinear and distinguished connections and metric structures. We construct the spinor differential geometry of locally anisotropic spaces and discuss some related issues connected with the geometric aspects of locally anisotropc interactions for gravitational, gauge, spinor, Dirac spinor and Proca fields. Motion equations in generalized Finsler spaces, of the mentioned type of fields, are defined in a geometric manner by using bundles of linear and affine frames locally adapted to the nonlinear connection structure. The nearly autoparallel maps are introduced as maps with deformation of connections extending the class of geodesic and conformal transforms. Using this approach we propose two variants of solution of the problem of definition of conservation laws on locally anisotropic spaces. 1991 Mathematics Subject Classification: 53A50, 53B15, 53B40, 53B50, 53C05, 70D10, 81D27, 81E13, 81E20, 83C40, 83C47, 83D05, 83E15 Key words and phrases: Spinors, nonlinear connections, generalized Lagrange and Finsler spaces, locally anisotropic fields, nearly autoparallel maps, conservation laws.

dg-ga↗