107 research outputs found
Cyclic and Ekpyrotic Universes in Modified Finsler Osculating Gravity on Tangent Lorentz Bundles
We consider models of accelerating Universe elaborated for Finsler like
gravity theories constructed on tangent bundles to Lorentz manifolds. In the
osculating approximation, certain locally anisotropic configurations are
similar to those for f(R) gravity. This allows us to generalize a proposal (by
Nojiri, Odintsov and Saez-Gomez, arXiv: 1108.0767) in order to reconstruct and
compare two classes of Einstein-Finsler gravity, EFG, and f(R) gravity theories
using modern cosmological data and realistic physical scenarios. We conclude
that EFG provides inflation, acceleration and little rip evolution scenarios
with realistic alternatives to standard Lambda CDM cosmology. The approach is
based on a proof that there is a general decoupling property of gravitational
field equations in EFG and modified theories which allows us to generate
off-diagonal cosmological solutions.Comment: latex2e, 28 pages, version accepted by CQG, with modifications and
additional explanations and new references requested by referee
Off-Diagonal Deformations of Kerr Metrics and Black Ellipsoids in Heterotic Supergravity
Geometric methods for constructing exact solutions of motion equations with
first order 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
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
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
On General Solutions for Field Equations in Einstein and Higher Dimension Gravity
We prove that the Einstein equations can be solved in a very general form for
arbitrary spacetime dimensions and various types of vacuum and non-vacuum cases
following a geometric method of anholonomic frame deformations for constructing
exact solutions in gravity. The main idea of this method is to introduce on
(pseudo) Riemannian manifolds an alternative (to the Levi-Civita connection)
metric compatible linear connection which is also completely defined by the
same metric structure. Such a canonically distinguished connection is with
nontrivial torsion which is induced by some nonholonomy frame coefficients and
generic off-diagonal terms of metrics. It is possible to define certain classes
of adapted frames of reference when the Einstein equations for such an
alternative connection transform into a system of partial differential
equations which can be integrated in very general forms. Imposing nonholonomic
constraints on generalized metrics and connections and adapted frames
(selecting Levi-Civita configurations), we generate exact solutions in Einstein
gravity and extra dimension generalizations.Comment: latex 2e, 11pt, 40 pages; it is a generalizaton with modified title,
including proofs and additional results for higher dimensional gravity of the
letter v1, on 14 pages; v4, with new abstract, modified title and up-dated
references is accepted by Int. J. Theor. Phy
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
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