554 research outputs found
Critical Remarks on Finsler Modifications of Gravity and Cosmology by Zhe Chang and Xin Li
I do not agree with the authors of papers arXiv:0806.2184 and
arXiv:0901.1023v1 (published in Phys. Lett., respectively, B668 (2008) 453 and
B676 (2009) 173). They consider that \textit{"In Finsler manifold, there exists
a unique linear connection - the Chern connection ... It is torsion freeness
and metric compatibility ... "}. There are well known results (for example,
presented in monographs by H. Rund and R. Miron and M. Anastasiei) that in
Finsler geometry there exist an infinite number of linear connections defined
by the same metric structure and that the Chern and Berwald connections
\textbf{are not metric compatible.} For instance, the Chern's one (being with
zero torsion and "weak" compatibility on the base manifold of tangent bundle)
is not generally compatible with the metric structure on total space. This
results in a number of additional difficulties and sophistication in definition
of Finsler spinors and Dirac operators and in additional problems with further
generalizations for quantum gravity and noncommutative/string/brane/gauge
theories. I conclude that standard physics theories can be generalized
naturally by gravitational and matter field equations for the Cartan and/or any
other Finsler metric compatible connections. This allows us to construct more
realistic models of Finsler spacetimes, anisotropic field interactions and
cosmology.Comment: latex2e, 11pt, 13 pages, v2 with updated references and typos
corrections, accepted to Phys. Lett.
The Entropy of Lagrange-Finsler Spaces and Ricci Flows
We formulate a statistical analogy of regular Lagrange mechanics and Finsler
geometry derived from Grisha Perelman's functionals generalized for
nonholonomic Ricci flows. There are elaborated explicit constructions when
nonholonomically constrained flows of Riemann metrics result in Finsler like
configurations, and inversely, and geometric mechanics is modelled on Riemann
spaces with preferred nonholonomic frame structure.Comment: latex2e, 20 pages, v3, the variant accepted to Rep. Math. Phy
Wormholes and Off-Diagonal Solutions in f(R,T), Einstein and Finsler Gravity Theories
The aims of this work are 1) to sketch a proof that there are such
parameterizations of the local frame and canonical connection structures when
the gravitational field equations in f(R,T)-modified gravity, MG, can be
integrated in generic off-diagonal forms with metrics depending on all
spacetime coordinates and 2) to provide some examples of exact solutions.Comment: 4 pages, ERE2012-Proceedings macros, Contribution to the Spanish
Relativity Meeting in Portugal, Guimaraes, September 3-7, 201
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
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 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.Comment: latex 2e, 11pt, 35 pages with table of content; version 2 modified
following Editor's requests and accepted to EPJ
Modified Dynamical Supergravity Breaking and Off-Diagonal Super-Higgs Effects
We argue that generic off-diagonal vacuum and nonvacuum solutions for
Einstein manifolds mimic physical effects in modified gravity theories (MGTs)
and encode certain models of the , Ho\v{r}ava type with dynamical
Lorentz symmetry breaking, induced effective mass for the graviton etc. Our
main goal is to investigate the dynamical breaking of local supersymmetry
determined by off-diagonal solutions in MGTs and encoded as effective Einstein
spaces. This includes the Deser-Zumino super-Higgs effect, for instance, for a
one-loop potential in a (simple but representative) model of supergravity. We develop and apply new geometrical techniques which allows
us to decouple the gravitational field equations and integrate them in a very
general form with the metric and vielbein fields depending on all the spacetime
coordinates via means of various generating and integration functions and
parameters. We study how solutions in MGTs may be related to the dynamical
generation of a gravitino mass and supersymmetry breaking.Comment: latex2e, 33 pages, with table of content; v3 accepted to Class.
Quant. Gravit
Ellipsoidal, Cylindrical, Bipolar and Toroidal Wormholes in 5D Gravity
In this paper we construct and analyze new classes of wormhole and flux
tube-like solutions for the 5D vacuum Einstein equations. These 5D solutions
possess generic local anisotropy which gives rise to a gravitational running or
scaling of the Kaluza-Klein ``electric'' and ``magnetic'' charges of these
solutions. It is also shown that it is possible to self-consistently construct
these anisotropic solutions with various rotational 3D hypersurface geometries
(i.e. ellipsoidal, cylindrical, bipolar and toroidal). The local anisotropy of
these solutions is handled using the technique of anholonomic frames with their
associated nonlinear connection structures [vst]. Through the use of the
anholonomic frames the metrics are diagonalized, in contrast to holonomic
coordinate frames where the metrics would have off-diagonal components. In the
local isotropic limit these solutions are shown to be equivalent to spherically
symmetric 5D wormhole and flux tube solutions.Comment: 27 pages ReVTeX, added references and discussion. To be published in
J. Math. Phy
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
Deformation Quantization of Nonholonomic Almost Kahler Models and Einstein Gravity
Nonholonomic distributions and adapted fame structures on (pseudo) Riemannian
manifolds of even dimension are employed to build structures equivalent to
almost Kahler geometry and which allows to perform a Fedosov-like quantization
of gravity. The nonlinear connection formalism that was formally elaborated for
Lagrange and Finsler geometry is implemented in classical and quantum Einstein
gravity.Comment: latex 2e, 11pt, 15 pages, v4 accepted by Phys. Lett.
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