Nonholonomic Black Ring and Solitonic Solutions in Finsler and Extra Dimension Gravity Theories

We study stationary configurations mimicking nonholonomic locally anisotropic black rings (for instance, with ellipsoidal polarizations and/or imbedded into solitonic backgrounds) in three/six dimensional pseudo-Finsler/ Riemannian spacetimes. In the asymptotically flat limit, for holonomic configurations, a subclass of such spacetimes contains the set of five dimensional black ring solutions with regular rotating event horizon. For corresponding parameterizations, the metrics and connections define Finsler-Einstein geometries modeled on tangent bundles, or on nonholonomic (pseudo) Riemannian manifolds. In general, there are vacuum nonholonomic gravitational configurations which can not be generated in the limit of zero cosmological constant.Comment: latex 2e, 11pt, 23 pages, v3, typos corrected and updated references; to be published in Int. J. Theor. Phys. (2010

Super-Luminal Effects for Finsler Branes as a Way to Preserve the Paradigm of Relativity Theories

Using Finsler brane solutions [see details and methods in: S. Vacaru, Class. Quant. Grav. 28 (2011) 215001], we show that neutrinos may surpass the speed of light in vacuum which can be explained by trapping effects from gravity theories on eight dimensional (co) tangent bundles on Lorentzian manifolds to spacetimes in general and special relativity. In nonholonomic variables, the bulk gravity is described by Finsler modifications depending on velocity/ momentum coordinates. Possible super-luminal phenomena are determined by the width of locally anisotropic brane (spacetime) and induced by generating functions and integration functions and constants in coefficients of metrics and nonlinear connections. We conclude that Finsler brane gravity trapping mechanism may explain neutrino super-luminal effects and almost preserve the paradigm of Einstein relativity as the standard one for particle physics and gravity.Comment: latex2e, 15 pages, v3, accepted to: Foundations of Physics 43 (2013

General very special relativity in Finsler cosmology

General very special relativity (GVSR) is the curved space-time of very special relativity (VSR) proposed by Cohen and Glashow. The geometry of general very special relativity possesses a line element of Finsler geometry introduced by Bogoslovsky. We calculate the Einstein field equations and derive a modified Friedmann-Robertson-Walker cosmology for an osculating Riemannian space. The Friedmann equation of motion leads to an explanation of the cosmological acceleration in terms of an alternative non-Lorentz invariant theory. A first order approach for a primordial-spurionic vector field introduced into the metric gives back an estimation of the energy evolution and inflation. © 2009 The American Physical Society

Friedman-like Robertson-Walker model in generalized metric space-time with weak anisotropy

A generalized FRW model of space-time is studied, taking into consideration the anisotropic structure of fields which are depended on the position and the direction (velocity). The Raychaudhouri and Friedman-like equations are investigated assuming the Finslerian character of space-time. A long range vector field of cosmological origin is considered in relation to a physical geometry where the Cartan connection has a fundamental role. The Friedman equations are produced including extra anisotropic terms. The variation of anisotropy z t is expressed in terms of the Cartan torsion tensor of the Finslerian manifold. A physical generalization of the Hubble and other cosmological parameters arises as a direct consequence of the equations of motion. © 2007 Springer Science+Business Media, LLC

Relativistic Finsler geometry

We briefly review some basic concepts of parallel displacement in Finsler geometry. In general relativity, the parallel translation of objects along the congruence of the fundamental observer corresponds to the evolution in time. By dropping the quadratic restriction on the measurement of an infinitesimal distance, the geometry is generalized to a Finsler structure. Apart from curvature, a new property of the manifold complicates the geometrodynamics, the color. The color brings forth an intrinsic local anisotropy, and many quantities depend on position and to a 'supporting' direction. We discuss this direction dependence and some physical interpretations. Also, we highlight that in Finsler geometry the parallel displacement is not necessarily always along the 'supporting' direction. The latter is a fundamental congruence of the manifold and induces a natural 1 + 3 decomposition. Its internal deformation is given through the evolution of the irreducible components of vorticity, shear, and expansion. © 2013 John Wiley & Sons, Ltd

Imperfect fluids, Lorentz violations, and Finsler cosmology

We construct a cosmological toy model based on a Finslerian structure of space-time. In particular, we are interested in a specific Finslerian Lorentz violating theory based on a curved version of Cohen and Glashow's very special relativity. The osculation of a Finslerian manifold to a Riemannian manifold leads to the limit of relativistic cosmology, for a specified observer. A modified flat Friedmann-Robertson-Walker cosmology is produced. The analogue of a zero energy particle unfolds some special properties of the dynamics. The kinematical equations of motion are affected by local anisotropies. Seeds of Lorentz violations may trigger density inhomogeneities to the cosmological fluid. © 2010 The American Physical Society

Resembling dark energy and modified gravity with Finsler-Randers cosmology

In this article we present the cosmological equivalence between the relativistic Finsler-Randers cosmology and the dark energy and modified gravity constructions at the background level. Starting from a small deviation from the quadraticity of the Riemannian geometry, through which the local structure of general relativity is modified and the curvature theory is extended, we extract the modified Friedmann equation. The corresponding extended Finsler-Randers cosmology is very interesting, and it can mimic dark energy and modified gravity, describing a large class of scale-factor evolutions, from inflation to late-time acceleration, including the phantom regime. In this respect, the nontrivial Universe evolution is not attributed to a new scalar field, or to gravitational modification, but it arises from the modification of the geometry itself. © 2013 American Physical Society