93 research outputs found
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
Fedosov Quantization of Lagrange-Finsler and Hamilton-Cartan Spaces and Einstein Gravity Lifts on (Co) Tangent Bundles
We provide a method of converting Lagrange and Finsler spaces and their
Legendre transforms to Hamilton and Cartan spaces into almost Kaehler
structures on tangent and cotangent bundles. In particular cases, the Hamilton
spaces contain nonholonomic lifts of (pseudo) Riemannian / Einstein metrics on
effective phase spaces. This allows us to define the corresponding Fedosov
operators and develop deformation quantization schemes for nonlinear mechanical
and gravity models on Lagrange- and Hamilton-Fedosov manifolds.Comment: latex2e, 11pt, 35 pages, v3, accepted to J. Math. Phys. (2009
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
Dirac Spinor Waves and Solitons in Anisotropic Taub-NUT Spaces
We apply a new general method of anholonomic frames with associated nonlinear
connection structure to construct new classes of exact solutions of
Einstein-Dirac equations in five dimensional (5D)gravity. Such solutions are
parametrized by off-diagonal metrics in coordinate (holonomic) bases, or,
equivalently, by diagonal metrics given with respect to some anholonomic frames
(pentads, or funfbiends, satisfing corresponding constraint relations). We
consider two possibilities of generalization of the Taub NUT metric in order to
obtain vacuum solutions of 5D Einsitein equations with effective
renormalization of constants having distinguished anisotropies on an angular
parameter or on extra dimension coordinate. The constructions are extended to
solutions describing self-consistent propagations of 3D Dirac wave packets in
5D anisotropic Taub NUT spacetimes. We show that such anisotropic
configurations of spinor matter can induce gravitational 3D solitons being
solutions of Kadomtsev-Petviashvili or of sine-Gordon equations.Comment: revtex, 16 pages, version 4, affiliation changed, accepted to CQ
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
Finsler and Lagrange Geometries in Einstein and String Gravity
We review the current status of Finsler-Lagrange geometry and
generalizations. The goal is to aid non-experts on Finsler spaces, but
physicists and geometers skilled in general relativity and particle theories,
to understand the crucial importance of such geometric methods for applications
in modern physics. We also would like to orient mathematicians working in
generalized Finsler and Kahler geometry and geometric mechanics how they could
perform their results in order to be accepted by the community of ''orthodox''
physicists.
Although the bulk of former models of Finsler-Lagrange spaces where
elaborated on tangent bundles, the surprising result advocated in our works is
that such locally anisotropic structures can be modelled equivalently on
Riemann-Cartan spaces, even as exact solutions in Einstein and/or string
gravity, if nonholonomic distributions and moving frames of references are
introduced into consideration.
We also propose a canonical scheme when geometrical objects on a (pseudo)
Riemannian space are nonholonomically deformed into generalized Lagrange, or
Finsler, configurations on the same manifold. Such canonical transforms are
defined by the coefficients of a prime metric and generate target spaces as
Lagrange structures, their models of almost Hermitian/ Kahler, or nonholonomic
Riemann spaces.
Finally, we consider some classes of exact solutions in string and Einstein
gravity modelling Lagrange-Finsler structures with solitonic pp-waves and
speculate on their physical meaning.Comment: latex 2e, 11pt, 44 pages; accepted to IJGMMP (2008) as a short
variant of arXiv:0707.1524v3, on 86 page
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
Ellipsoidal shapes in general relativity: general definitions and an application
A generalization of the notion of ellipsoids to curved Riemannian spaces is
given and the possibility to use it in describing the shapes of rotating bodies
in general relativity is examined. As an illustrative example, stationary,
axisymmetric perfect-fluid spacetimes with a so-called confocal inside
ellipsoidal symmetry are investigated in detail under the assumption that the
4-velocity of the fluid is parallel to a time-like Killing vector field. A
class of perfect-fluid metrics representing interior NUT-spacetimes is obtained
along with a vacuum solution with a non-zero cosmological constant.Comment: Latex, 22 pages, Revised version accepted in Class. Quantum. Grav.,
references adde
Nonholonomic Ricci Flows, Exact Solutions in Gravity, and Symmetric and Nonsymmetric Metrics
We provide a proof that nonholonomically constrained Ricci flows of (pseudo)
Riemannian metrics positively result into nonsymmetric metrics (as explicit
examples, we consider flows of some physically valuable exact solutions in
general relativity). There are constructed and analyzed three classes of
solutions of Ricci flow evolution equations defining nonholonomic deformations
of Taub NUT, Schwarzschild, solitonic and pp--wave symmetric metrics into
nonsymmetric ones.Comment: latex2e, 12pt, 40 pages, version 2 with minor modifications, to be
published in Int. J. Theor. Phy
On the Dirac Eigenvalues as Observables of the on-shell N=2 D=4 Euclidean Supergravity
We generalize previous works on the Dirac eigenvalues as dynamical variables
of the Euclidean gravity and N=1 D=4 supergravity to on-shell N=2 D=4 Euclidean
supergravity. The covariant phase space of the theory is defined as as the
space of the solutions of the equations of motion modulo the on-shell gauge
transformations. In this space we define the Poisson brackets and compute their
value for the Dirac eigenvalues.Comment: 10 pages, LATeX fil
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