1,661 research outputs found
On General Solutions of Einstein Equations
We show how the Einstein equations with cosmological constant (and/or various
types of matter field sources) can be integrated in a very general form
following the anholonomic deformation method for constructing exact solutions
in four and five dimensional gravity (S. Vacaru, IJGMMP 4 (2007) 1285). In this
letter, we prove that such a geometric method can be used for constructing
general non-Killing solutions. The key idea is to introduce an auxiliary linear
connection which is also metric compatible and completely defined by the metric
structure but contains some torsion terms induced nonholonomically by generic
off-diagonal coefficients of metric. There are some classes of nonholonomic
frames with respect to which the Einstein equations (for such an auxiliary
connection) split into an integrable system of partial differential equations.
We have to impose additional constraints on generating and integration
functions in order to transform the auxiliary connection into the Levi-Civita
one. This way, we extract general exact solutions (parametrized by generic
off-diagonal metrics and depending on all coordinates) in Einstein gravity and
five dimensional extensions.Comment: 15 pages, latex2e, submitted to arXiv.org on September 22, 2009,
equivalent to arXiv: 0909.3949v1 [gr-qc]; an extended/modified variant
published in IJTP 49 (2010) 884-913, equivalent to arXiv: 0909.3949v4 [gr-qc
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
Domain wall tilting in the presence of the Dzyaloshinskii-Moriya interaction in out-of-plane magnetized magnetic nanotracks
We show that the Dzyaloshinskii-Moriya interaction (DMI) can lead to a
tilting of the domain wall (DW) surface in perpendicularly magnetized magnetic
nanotracks when DW dynamics is driven by an easy axis magnetic field or a spin
polarized current. The DW tilting affects the DW dynamics for large DMI and the
tilting relaxation time can be very large as it scales with the square of the
track width. The results are well explained by an analytical model based on a
Lagrangian approach where the DMI and the DW tilting are included. We propose a
simple way to estimate the DMI in a magnetic multilayers by measuring the
dependence of the DW tilt angle on a transverse static magnetic field. Our
results shed light on the current induced DW tilting observed recently in Co/Ni
multilayers with inversion asymmetry, and further support the presence of DMI
in these systems.Comment: 12 pages, 3 figures, 1 Supplementary Material
Nonholonomic Ricci Flows: II. Evolution Equations and Dynamics
This is the second paper in a series of works devoted to nonholonomic Ricci
flows. By imposing non-integrable (nonholonomic) constraints on the Ricci flows
of Riemannian metrics we can model mutual transforms of generalized
Finsler-Lagrange and Riemann geometries. We verify some assertions made in the
first partner paper and develop a formal scheme in which the geometric
constructions with Ricci flow evolution are elaborated for canonical nonlinear
and linear connection structures. This scheme is applied to a study of
Hamilton's Ricci flows on nonholonomic manifolds and related Einstein spaces
and Ricci solitons. The nonholonomic evolution equations are derived from
Perelman's functionals which are redefined in such a form that can be adapted
to the nonlinear connection structure. Next, the statistical analogy for
nonholonomic Ricci flows is formulated and the corresponding thermodynamical
expressions are found for compact configurations. Finally, we analyze two
physical applications: the nonholonomic Ricci flows associated to evolution
models for solitonic pp-wave solutions of Einstein equations, and compute the
Perelman's entropy for regular Lagrange and analogous gravitational systems.Comment: v2 41 pages, latex2e, 11pt, the variant accepted by J. Math. Phys.
with former section 2 eliminated, a new section 5 with applications in
gravity and geometric mechanics, and modified introduction, conclusion and
new reference
Electric-field control of domain wall nucleation and pinning in a metallic ferromagnet
The electric (E) field control of magnetic properties opens the prospects of
an alternative to magnetic field or electric current activation to control
magnetization. Multilayers with perpendicular magnetic anisotropy (PMA) have
proven to be particularly sensitive to the influence of an E-field due to the
interfacial origin of their anisotropy. In these systems, E-field effects have
been recently applied to assist magnetization switching and control domain wall
(DW) velocity. Here we report on two new applications of the E-field in a
similar material : controlling DW nucleation and stopping DW propagation at the
edge of the electrode
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
Jacobi stability of the vacuum in the static spherically symmetric brane world models
We analyze the stability of the structure equations of the vacuum in the
brane world models, by using both the linear (Lyapunov) stability analysis, and
the Jacobi stability analysis, the Kosambi-Cartan-Chern (KCC) theory. In the
brane world models the four dimensional effective Einstein equations acquire
extra terms, called dark radiation and dark pressure, respectively, which arise
from the embedding of the 3-brane in the bulk. Generally, the spherically
symmetric vacuum solutions of the brane gravitational field equations, have
properties quite distinct as compared to the standard black hole solutions of
general relativity. We close the structure equations by assuming a simple
linear equation of state for the dark pressure. In this case the vacuum is
Jacobi stable only for a small range of values of the proportionality constant
relating the dark pressure and the dark radiation. The unstable trajectories on
the brane behave chaotically, in the sense that after a finite radial distance
it would be impossible to distinguish the trajectories that were very near each
other at an initial point. Hence the Jacobi stability analysis offers a
powerful method for constraining the physical properties of the vacuum on the
brane.Comment: 21 pages, 3 figures, accepted for publication in PR
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
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
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