Locally Anisotropic Wormholes and Flux Tubes in 5D Gravity

In this article we examine a class of wormhole and flux tube like solutions to 5D vacuum Einstein equations. These solutions possess generic local anisotropy, and their local isotropic limit is shown to be conformally equivalent to the spherically symmetric 5D solutions of gr-qc/9807086. The anisotropic solutions investigated here have two physically distinct signatures: First, they can give rise to angular-dependent, anisotropic ``electromagnetic'' interactions. Second, they can result in a gravitational running of the ``electric'' and ``magnetic'' charges of the solutions. This gravitational running of the electromagnetic charges is linear rather than logarithmic, and could thus serve as an indirect signal for the presence of higher dimensions. The local anisotropy of these solutions is modeled using the technique of anholonomic frames with respect to which the metrics are diagonalized. If holonomic coordinates frames were used then such metrics would have off-diagonal components.Comment: 14 pages, revtex, references added, extra section added giving physical motivation for the solutions. To be published in PL

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.Comment: 37 page

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

Geometric methods for constructing exact solutions of motion equations with first order $\alpha ^{\prime}$ corrections to the heterotic supergravity action implying a non-trivial Yang-Mills sector and six dimensional, 6-d, almost-K\"ahler 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-K\"ahler 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.Comment: latex2e, 44 pages with table of content, v2 accepted to EJPC with minor typos modifications requested by editor and referee and up-dated reference

Fractional Dynamics from Einstein Gravity, General Solutions, and Black Holes

We study the fractional gravity for spacetimes with non-integer dimensions. Our constructions are based on a geometric formalism with the fractional Caputo derivative and integral calculus adapted to nonolonomic distributions. This allows us to define a fractional spacetime geometry with fundamental geometric/physical objects and a generalized tensor calculus all being similar to respective integer dimension constructions. Such models of fractional gravity mimic the Einstein gravity theory and various Lagrange-Finsler and Hamilton-Cartan generalizations in nonholonomic variables. The approach suggests a number of new implications for gravity and matter field theories with singular, stochastic, kinetic, fractal, memory etc processes. We prove that the fractional gravitational field equations can be integrated in very general forms following the anholonomic deformation method for constructing exact solutions. Finally, we study some examples of fractional black hole solutions, fractional ellipsoid gravitational configurations and imbedding of such objects in fractional solitonic backgrounds.Comment: latex2e, 11pt, 40 pages with table of conten

Finsler Branes and Quantum Gravity Phenomenology with Lorentz Symmetry Violations

A consistent theory of quantum gravity (QG) at Planck scale almost sure contains manifestations of Lorentz local symmetry violations (LV) which may be detected at observable scales. This can be effectively described and classified by models with nonlinear dispersions and related Finsler metrics and fundamental geometric objects (nonlinear and linear connections) depending on velocity/ momentum variables. We prove that the trapping brane mechanism provides an accurate description of gravitational and matter field phenomena with LV over a wide range of distance scales and recovering in a systematic way the general relativity (GR) and local Lorentz symmetries. In contrast to the models with extra spacetime dimensions, the Einstein-Finsler type gravity theories are positively with nontrivial nonlinear connection structure, nonholonomic constraints and torsion induced by generic off-diagonal coefficients of metrics, and determined by fundamental QG and/or LV effects.Comment: latex2e, 11pt, 34 pages, the version accepted to Class. Quant. Gra

Two-Connection Renormalization and Nonholonomic Gauge Models of Einstein Gravity

A new framework to perturbative quantum gravity is proposed following the geometry of nonholonomic distributions on (pseudo) Riemannian manifolds. There are considered such distributions and adapted connections, also completely defined by a metric structure, when gravitational models with infinite many couplings reduce to two--loop renormalizable effective actions. We use a key result from our partner work arXiv:0902.0911 that the classical Einstein gravity theory can be reformulated equivalently as a nonholonomic gauge model in the bundle of affine/de Sitter frames on pseudo-Riemannian spacetime. It is proven that (for a class of nonholonomic constraints and splitting of the Levi-Civita connection into a "renormalizable" distinguished connection, on a base background manifold, and a gauge like distortion tensor, in total space) a nonholonomic differential renormalization procedure for quantum gravitational fields can be elaborated. Calculation labor is reduced to one- and two-loop levels and renormalization group equations for nonholonomic configurations.Comment: latex2e, 40 pages, v4, accepted for Int. J. Geom. Meth. Mod. Phys. 7 (2010

New Classes of Off-Diagonal Cosmological Solutions in Einstein Gravity

In this work, we apply the anholonomic deformation method for constructing new classes of anisotropic cosmological solutions in Einstein gravity and/or generalizations with nonholonomic variables. There are analyzed four types of, in general, inhomogeneous metrics, defined with respect to anholonomic frames and their main geometric properties. Such spacetimes contain as particular cases certain conformal and/or frame transforms of the well known Friedman-Robertson-Walker, Bianchi, Kasner and Godel universes and define a great variety of cosmological models with generic off-diagonal metrics, local anisotropy and inhomogeneity. It is shown that certain nonholonomic gravitational configurations may mimic de Sitter like inflation scenaria and different anisotropic modifications without satisfying any classical false-vacuum equation of state. Finally, we speculate on perspectives when such off-diagonal solutions can be related to dark energy and dark matter problems in modern cosmology.Comment: latex2e, 11pt, 33 pages with table of content, a variant accepted to IJT

Clifford-Finsler Algebroids and Nonholonomic Einstein-Dirac Structures

We propose a new framework for constructing geometric and physical models on nonholonomic manifolds provided both with Clifford -- Lie algebroid symmetry and nonlinear connection structure. Explicit parametrizations of generic off-diagonal metrics and linear and nonlinear connections define different types of Finsler, Lagrange and/or Riemann-Cartan spaces. A generalization to spinor fields and Dirac operators on nonholonomic manifolds motivates the theory of Clifford algebroids defined as Clifford bundles, in general, enabled with nonintegrable distributions defining the nonlinear connection. In this work, we elaborate the algebroid spinor differential geometry and formulate the (scalar, Proca, graviton, spinor and gauge) field equations on Lie algebroids. The paper communicates new developments in geometrical formulation of physical theories and this approach is grounded on a number of previous examples when exact solutions with generic off-diagonal metrics and generalized symmetries in modern gravity define nonholonomic spacetime manifolds with uncompactified extra dimensions.Comment: The manuscript was substantially modified following recommendations of JMP referee. The former Chapter 2 and Appendix were elliminated. The Introduction and Conclusion sections were modifie

Exact accelerating solitons in nonholonomic deformation of the KdV equation with two-fold integrable hierarchy

Recently proposed nonholonomic deformation of the KdV equation is solved through inverse scattering method by constructing AKNS-type Lax pair. Exact and explicit N-soliton solutions are found for the basic field and the deforming function showing an unusual accelerated (decelerated) motion. A two-fold integrable hierarchy is revealed, one with usual higher order dispersion and the other with novel higher nonholonomic deformations.Comment: 7 pages, 2 figures, latex. Exact explicit exact N-soliton solutions (through ISM) for KdV field u and deforming function w are included. Version to be published in J. Phys.