arXiv subjects

Sergiu I. Vacaru

Publications and source records attributed to Sergiu I. Vacaru.

At least 55 records · Page 3Linked to original sources

arXiv2015

Off-Diagonal Ekpyrotic Scenarios and Equivalence of Modified, Massive and/or Einstein Gravity

Using our anholonomic frame deformation method, we show how generic off-diagonal cosmological solutions depending, in general, on all spacetime coordinates and undergoing a phase of ultra-slow contraction can be constructed in massive gravity. In this paper, there are found and studied new classes of locally anisotropic and (in) homogeneous cosmological metrics with open and closed spatial geometries. The late time acceleration is present due to effective cosmological terms induced by nonlinear off-diagonal interactions and graviton mass. The off-diagonal cosmological metrics and related St\" uckelberg fields are constructed in explicit form up to nonholonomic frame transforms of the Friedmann-Lamaître-Robertson-Walker (FLRW) coordinates. We show that the solutions include matter, graviton mass and other effective sources modelling nonlinear gravitational and matter fields interactions in modified and/or massive gravity, with polarization of physical constants and deformations of metrics, which may explain certain dark energy and dark matter effects. There are stated and analyzed the conditions when such configurations mimic interesting solutions in general relativity and modifications and recast the general Painlevé--ullstrand and FLRW metrics. Finally, we elaborate on a reconstruction procedure for a subclass of off-diagonal cosmological solutions which describe cyclic and ekpyrotic universes, with an emphasis on open issues and observable signatures.

hep-th↗

arXiv2015

Effective Einstein Cosmological Spaces for Non-Minimal Modified Gravity

Certain off-diagonal vacuum and nonvacuum configurations in Einstein gravity can mimic physical effects of modified gravitational theories of $ f(R,T,R_{μν}T^{μν})$ type. We prove this statement by constructing exact and approximate solutions which encode certain models of covariant Ho\v rava type gravity with dynamical Lorentz symmetry breaking. Off-diagonal generalizations of de Sitter and nonolonomic $Λ$CDM universes are constructed which are generated through nonlinear gravitational polarization of fundamental physical constants and which model interactions with non-constant exotic fluids and effective matter. The problem of possible matter instability for such off-diagonal deformations in (modified) gravity theories is discussed.

math-ph↗

arXiv2015

Einstein Spaces Modeling Nonminimal Modified Gravity

Off-diagonal vacuum and nonvacuum configurations in Einstein gravity can mimic physical effects of modified gravitational theories of $f(R,T,R_{μν}T^{μν})$ type. To prove this statement, exact and approximate solutions are constructed in the review, which encode certain models of covariant Hořava type gravity with dynamical Lorentz symmetry breaking. The corresponding FLRW cosmological dynamics with possible nonholonomic deformations and the reconstruction procedure of certain actions closely related with the standard $Λ$CDM universe are studied. Off-diagonal generalizations of de Sitter universes are constructed which are generated through nonlinear gravitational polarization of fundamental physical constants and which model interactions with non-constant exotic fluids and effective matter. The problem of possible matter instability for such off-diagonal deformations in (modified) gravity theories is briefly discussed.

gr-qc↗

arXiv2015

Black Ring and Kerr Ellipsoid - Solitonic Configurations in Modified Finsler Gravity

We study an effective Einstein-Finsler theory on tangent Lorentz bundle constructed as a "minimal" extension of general relativity. Black ring and Kerr like ellipsoid exact solutions and soliton configurations are presented. In this endeavor the relevant metric depends not only on four dimensional spacetime coordinates and also on velocity type variables that can be interpreted as additional coordinates in the space of "extra dimensions".

gr-qc↗

arXiv2015

Equivalent off-diagonal cosmological models and ekpyrotic scenarios in f(R)-modified, massive and Einstein gravity

We re-investigate how generic off-diagonal cosmological solutions depending, in general, on all spacetime coordinates can be constructed in massive and f-modified gravity using the anholonomic frame deformation method. There are constructed new classes of locally anisotropic and (in) homogeneous cosmological metrics with open and closed spatial geometries. By resorting such solutions, we show that they describe the late time acceleration due to effective cosmological terms induced by nonlinear off-diagonal interactions, possible modifications of the gravitational action and graviton mass. The cosmological metrics and related St\" uckelberg fields are constructed in explicit form up to nonholonomic frame transforms of the Friedmann-Lama\^ıtre-Robertson-Walker (FLRW) coordinates. The solutions include matter, graviton mass and other effective sources modelling nonlinear gravitational and matter fields interactions with polarization of physical constants and deformations of metrics, which may explain dark energy and dark matter effects. However, we argue that it is not obligatory always to modify gravity if we consider effective generalized Einstein equations with nontrivial vacuum and/or non-minimal coupling with matter. Indeed, we state certain conditions when such configurations mimic interesting solutions in general relativity and modifications, for instance, when we can extract the general Painlev\' e-Gullstrand and FLRW metrics. In a more general context, we elaborate on a reconstruction procedure for off-diagonal cosmological solutions which describe cyclic and ekpyrotic universes. Finally, there are discussed open issues and further perspectives.

gr-qc↗

arXiv2015

Generic Off--Diagonal Solutions and Solitonic Hierarchies in Einstein and Modified Gravity

We summarize some our recent results on encoding exact solutions of field equations in Einstein and modified gravity theories into solitonic hierarchies derived for nonholonomic curve flows with associated bi-Hamilton structure. We argue that there is a canonical distinguished connection for which the fundamental geometric/ physical equations decouple in general form. This allows us to construct very general classes of generic off-diagonal solutions determined by corresponding types of generating and integration functions depending on all (spacetime) coordinates. If the integral varieties are constrained to zero torsion configurations, we can extract solutions for the general relativity theory. We conclude that the geometric and physical data for various classes of effective/modified Einstein spaces can be encoded into multi-component versions of the sine-Gordon, or modified Korteweg - de Vries equations.

gr-qc↗

arXiv2014

A geometric method of constructing exact solutions in modified f(R,T)-gravity with Yang-Mills and Higgs interactions

We show that a geometric techniques can be elaborated and applied for constructing generic off-diagonal exact solutions in $f(R,T)$--modified gravity for systems of gravitational-Yang-Mills-Higgs equations. The corresponding classes of metrics and generalized connections are determined by generating and integration functions which depend, in general, on all space and time coordinates and may possess, or not, Killing symmetries. For nonholonomic constraints resulting in Levi-Civita configurations, we can extract solutions of the Einstein-Yang-Mills-Higgs equations. We show that the constructions simplify substantially for metrics with at least one Killing vector. There are provided and analyzed some examples of exact solutions describing generic off-diagonal modifications to black hole/ellipsoid and solitonic configurations.

gr-qc↗

arXiv2014

Off-Diagonal Deformations of Kerr Black Holes in Einstein and Modified Massive Gravity and Higher Dimensions

We find general parameterizations for generic off-diagonal spacetime metrics and matter sources in general relativity (GR) and modified gravity theories when the field equations decouple with respect to certain types of 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. Our method can be extended to higher dimensions which simplifies some proofs for embedded and nonholonomically constrained four-dimensional configurations. We reproduce the Kerr solution and show how to deform it nonholonomically into new classes of generic off-diagonal solutions depending on 3-8 spacetime coordinates. Certain examples of exact solutions are analyzed and that are determined by contributions of new type of interactions with sources in massive gravity and/or modified f(R,T) gravity. We conclude that by 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.

gr-qc↗

arXiv2014

Ghost-Free Massive $f(R)$ Theories Modelled as Effective Einstein Spaces and Cosmic Acceleration

We study how massive ghost-free gravity $f(R)$-modified theories, MGFTs, can be encoded into generic off-diagonal Einstein spaces. Using "auxiliary" connections completely defined by the metric fields and adapted to nonholonomic frames with associated nonlinear connection structure, we decouple and integrate in certain general forms the field equations in MGFT. Imposing additional nonholonomic constraints, we can generate Levi-Civita, LC, configurations and mimic MGFT effects via off-diagonal interactions of effective Einstein and/or Einstein-Cartan gravity with nonholonomically induced torsion. We show that imposing nonholonomic constraints it is possible reproduce very specific models of massive $f(R)$ gravity studied in \cite{sarid,odintsr}. The cosmological evolution of ghost-free off-diagonal Einstein spaces is investigated. Certain compatibility of MGFT cosmology to small off--diagonal deformations of $Λ$CDM models is established.

physics.gen-ph↗

arXiv2014

Spinor and Twistor Geometry in Einstein Gravity and Finsler Modifications

We present a generalization of the spinor and twistor geometry for on (pseudo) Riemannian manifolds enabled with nonholonomic distributions or for Finsler-Cartan spaces modelled on tangent Lorentz bundles. Nonholonomic (Finsler) twistors are defined as solutions of generalized twistor equations determined by spin connections and frames adapted to nonlinear connection structures. We show that the constructions for local twistors can be globalized using nonholonomic deformations with "auxiliary" metric compatible connections completely determined by the metric structure and/or the Finsler fundamental function. We explain how to perform such an approach in the Einstein gravity theory formulated in Finsler like variables with conventional nonholonomic 2+2 splitting.

math-ph↗

arXiv2014

Modified Einstein and Finsler Like Theories on Tangent Lorentz Bundles

We study modifications of general relativity, GR, with nonlinear dispersion relations which can be geometrized on tangent Lorentz bundles. Such modified gravity theories, MGTs, can be modeled by gravitational Lagrange density functionals $f(\mathbf{R},\mathbf{T},F)$ with generalized/ modified scalar curvature $\mathbf{R}$, trace of matter field tensors $\mathbf{T}$ and modified Finsler like generating function $F$. In particular, there are defined extensions of GR with extra dimensional "velocity/ momentum" coordinates. For four dimensional models, we prove that it is possible to decouple and integrate in very general forms the gravitational fields for $f(\mathbf{R},\mathbf{T},F)$-modified gravity using nonholonomic 2+2 splitting and nonholonomic Finsler like variables $F$. We study the modified motion and Newtonian limits of massive test particles on nonlinear geodesics approximated with effective extra forces orthogonal to the four--velocity. We compute the constraints on the magnitude of extra-accelerations and analyze perihelion effects and possible cosmological implications of such theories. We also derive the extended Raychaudhuri equation in the framework of a tangent Lorentz bundle. Finally, we speculate on effective modelling of modified theories by generic off-diagonal configurations in Einstein and/or MGTs and Finsler gravity. We provide some examples for modified stationary (black) ellipsoid configurations and locally anisotropic solitonic backgrounds.

physics.gen-ph↗

arXiv2014

Almost Kaehler Ricci Flows and Einstein and Lagrange-Finsler Structures on Lie Algebroids

In this work we investigate Ricci flows of almost Kaehler structures on Lie algebroids when the fundamental geometric objects are completely determined by (semi) Riemannian metrics, or effective) regular generating Lagrange/ Finsler, functions. There are constructed canonical almost symplectic connections for which the geometric flows can be represented as gradient ones and characterized by nonholonomic deformations of Grigory Perelman's functionals. The first goal of this paper is to define such thermodynamical type values and derive almost Kähler - Ricci geometric evolution equations. The second goal is to study how fixed Lie algebroid, i.e. Ricci soliton, configurations can be constructed for Riemannian manifolds and/or (co) tangent bundles endowed with nonholonomic distributions modelling (generalized) Einstein or Finsler - Cartan spaces. Finally, there are provided some examples of generic off-diagonal solutions for Lie algebroid type Ricci solitons and (effective) Einstein and Lagrange-Finsler algebroids.

math.DG↗

arXiv2014

Exact Solutions in Modified Massive Gravity and Off-Diagonal Wormhole Deformations

There are explored off-diagonal deformations of "prime" metrics in Einstein gravity (for instance, for wormhole configurations) into "target" exact solutions in f(R,T)-modified and massive/ bi-metric gravity theories. The new classes of solutions may posses, or not, Killing symmetries and can be characterized by effective induced masses, anisotropic polarized interactions and cosmological constants. For nonholonomic deformations with (conformal) ellipsoid/ toroid and/or solitonic symmetries and, in particular, for small eccentricity rotoid configurations, we can generate wormholes like objects matching external black ellipsoid - de Sitter geometries. We conclude that there are nonholonomic transforms and/or non-trivial limits to exact solutions in general relativity when modified/ massive gravity effects are modeled by off-diagonal and/or nonholonomic parametric interactions.

gr-qc↗

arXiv2013

Decoupling of Field Equations in Einstein and Modified Gravity

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.

physics.gen-ph↗

arXiv2013

The Algebraic Index Theorem and Fedosov Quantization of Lagrange-Finsler and Einstein Spaces

Various types of Lagrange and Finsler geometries and the Einstein gravity theory, and modifications, can be modelled by nonholonomic distributions on tangent bundles/ manifolds when the fundamental geometric objects are adapted to nonlinear connection structures. We can convert such geometries and physical theories into almost Kahler/ Poisson structures on (co)tangent bundles. This allows us to apply the Fedosov quantization formalism to almost symplectic connections induced by Lagrange-Finsler and/or Einstein fundamental geometric objects. There are constructed respective nonholonomic versions of the trace density maps for the zeroth Hochschild homology of deformation quantization of distinguished algebras (in this work, adapted to nonlinear connection structure). Our main result consists in an algebraic index theorem for Lagrange-Finsler and Einstein spaces. Finally, we show how the Einstein field equations for gravity theories and geometric mechanics models can be imbedded into the formalism of deformation quantization and index theorem.

math-ph↗

arXiv2013

Covariant Renormalizable Modified and Massive Gravity Theories on (Non) Commutative Tangent Lorentz Bundles

The fundamental field equations in modified gravity (including general relativity; massive and bimetric theories; Ho\vrava-Lifshits, HL; Einstein--Finsler gravity extensions etc) posses an important decoupling property with respect to nonholonomic frames with 2 (or 3) +2+2+... spacetime decompositions. This allows us to construct exact solutions with generic off--diagonal metrics depending on all spacetime coordinates via generating and integration functions containing (un-) broken symmetry parameters. Such nonholonomic configurations/ models have a nice ultraviolet behavior and seem to be ghost free and (super) renormalizable in a sense of covariant and/or massive modifications of HL gravity. The apparent noncommutativity and breaking of Lorentz invariance by quantum effects can be encoded into fibers of noncommutative tangent Lorentz bundles for corresponding "partner" anisotropically induced theories. We show how the constructions can be extended to include conjectured covariant reonormalizable models with massive graviton fields and effective Einstein fields with (non)commutative variables.

physics.gen-ph↗

arXiv2013

Cosmological Solutions in Biconnection and Bimetric Gravity Theories

We show how generic off--diagonal cosmological solutions depending, in general, on all spacetime coordinates can be constructed in massive gravity using the anholonomic frame deformation method. Such metrics describe the late time acceleration due to effective cosmological terms induced by nonlinear off--diagonal interactions and graviton mass and include matter, graviton mass and other effective sources modelling nonlinear gravitational and matter fields interactions with polarization of physical constants and deformations of metrics, which may explain certain dark energy and dark matter effects.

gr-qc↗

arXiv2013

Covariant Renormalizable Gravity Theories on (Non) Commutative Tangent Bundles

The field equations in modified gravity theories possess an important decoupling property with respect to certain classes of nonholonomic frames. This allows us to construct generic off--diagonal solutions depending on all spacetime coordinates via generating and integration functions containing (un--)broken symmetry parameters. Some corresponding analogous models have a nice ultraviolet behavior and seem to be (super) renormalizable in a sense of covariant modifications of Hořava--Lifshits (HL) and ghost free gravity. The apparent noncommutativity and breaking of Lorentz invariance by quantum effects can be encoded into geometric objects and basic equations on noncommutative tangent Lorentz. The constructions can be extended to include conjectured covariant reonormalizable models with effective Einstein fields with (non)commutative variables.

gr-qc↗