2,606 research outputs found
Sparling two-forms, the conformal factor and the gravitational energy density of the teleparallel equivalent of general relativity
It has been shown recently that within the framework of the teleparallel
equivalent of general relativity (TEGR) it is possible to define the energy
density of the gravitational field. The TEGR amounts to an alternative
formulation of Einstein's general relativity, not to an alternative gravity
theory. The localizability of the gravitational energy has been investigated in
a number of space-times with distinct topologies, and the outcome of these
analises agree with previously known results regarding the exact expression of
the gravitational energy, and/or with the specific properties of the space-time
manifold. In this article we establish a relationship between the expression
for the gravitational energy density of the TEGR and the Sparling two-forms,
which are known to be closely connected with the gravitational energy. We also
show that our expression of energy yields the correct value of gravitational
mass contained in the conformal factor of the metric field.Comment: 12 pages, Latex file, no figures, to be published in Gen. Rel. Gra
On certain relationships between cosmological observables in the Einstein-Cartan gravity
We show that in the Einstein-Cartan gravity it is possible to obtain a
relation between Hubble's expansion and the global rotation (vorticity) of the
Universe. Gravitational coupling can be reduced to dimensionless quantity of
order unity, fixing the scalar mass density and the resulting negative
cosmological constant at spacelike infinity. Current estimates of the expansion
and rotation (see also astro-ph/9703082) of the Universe favour the massive
spinning particles as candidate particles for cold and hot dark matter. Nodland
and Ralston vorticity (Phys. Rev. Lett. 78 (1997) 3043) overestimates the value
favoured by the Einstein-Cartan gravity for three orders of magnitude.Comment: 7 pages, LaTeX styl
The Einstein 3-form G_a and its equivalent 1-form L_a in Riemann-Cartan space
The definition of the Einstein 3-form G_a is motivated by means of the
contracted 2nd Bianchi identity. This definition involves at first the complete
curvature 2-form. The 1-form L_a is defined via G_a = L^b \wedge #(o_b \wedge
o_a). Here # denotes the Hodge-star, o_a the coframe, and \wedge the exterior
product. The L_a is equivalent to the Einstein 3-form and represents a certain
contraction of the curvature 2-form. A variational formula of Salgado on
quadratic invariants of the L_a 1-form is discussed, generalized, and put into
proper perspective.Comment: LaTeX, 13 Pages. To appear in Gen. Rel. Gra
Mathematical structure of unit systems
We investigate the mathematical structure of unit systems and the relations
between them. Looking over the entire set of unit systems, we can find a
mathematical structure that is called preorder (or quasi-order). For some pair
of unit systems, there exists a relation of preorder such that one unit system
is transferable to the other unit system. The transfer (or conversion) is
possible only when all of the quantities distinguishable in the latter system
are always distinguishable in the former system. By utilizing this structure,
we can systematically compare the representations in different unit systems.
Especially, the equivalence class of unit systems (EUS) plays an important role
because the representations of physical quantities and equations are of the
same form in unit systems belonging to an EUS. The dimension of quantities is
uniquely defined in each EUS. The EUS's form a partially ordered set. Using
these mathematical structures, unit systems and EUS's are systematically
classified and organized as a hierarchical tree.Comment: 27 pages, 3 figure
A formal framework for a nonlocal generalization of Einstein's theory of gravitation
The analogy between electrodynamics and the translational gauge theory of
gravity is employed in this paper to develop an ansatz for a nonlocal
generalization of Einstein's theory of gravitation. Working in the linear
approximation, we show that the resulting nonlocal theory is equivalent to
general relativity with "dark matter". The nature of the predicted "dark
matter", which is the manifestation of the nonlocal character of gravity in our
model, is briefly discussed. It is demonstrated that this approach can provide
a basis for the Tohline-Kuhn treatment of the astrophysical evidence for dark
matter.Comment: 13 pages RevTex, no figures; v2: minor corrections, reference added,
matches published versio
On possible skewon effects on light propagation
We start from a local and linear spacetime relation between the
electromagnetic excitation and the field strength. Then we study the generally
covariant Fresnel surfaces for light rays and light waves. The metric and the
connection of spacetime are left unspecified. Accordingly, our framework is
ideally suited for a search of possible violations of the Lorentz symmetry in
the photon sector of the extended standard model. We discuss how the skewon
part of the constitutive tensor, if suitably parametrized, influences the
Fresnel surfaces and disturbs the light cones of vacuum electrodynamics.
Conditions are specified that yield the reduction of the original quartic
Fresnel surface to the double light cone structure (birefringence) and to the
single light cone. Qualitatively, the effects of the real skewon field can be
compared to those in absorbing material media. In contrast, the imaginary
skewon field can be interpreted in terms of non-absorbing media with natural
optical activity and Faraday effects. The astrophysical data on gamma-ray
bursts are used for deriving an upper limit for the magnitude of the skewon
field.Comment: Revtex, 29 pages, 10 figures, references added, text as in the
published versio
Non-equilibrium dynamics of stochastic point processes with refractoriness
Stochastic point processes with refractoriness appear frequently in the
quantitative analysis of physical and biological systems, such as the
generation of action potentials by nerve cells, the release and reuptake of
vesicles at a synapse, and the counting of particles by detector devices. Here
we present an extension of renewal theory to describe ensembles of point
processes with time varying input. This is made possible by a representation in
terms of occupation numbers of two states: Active and refractory. The dynamics
of these occupation numbers follows a distributed delay differential equation.
In particular, our theory enables us to uncover the effect of refractoriness on
the time-dependent rate of an ensemble of encoding point processes in response
to modulation of the input. We present exact solutions that demonstrate generic
features, such as stochastic transients and oscillations in the step response
as well as resonances, phase jumps and frequency doubling in the transfer of
periodic signals. We show that a large class of renewal processes can indeed be
regarded as special cases of the model we analyze. Hence our approach
represents a widely applicable framework to define and analyze non-stationary
renewal processes.Comment: 8 pages, 4 figure
Enhancement of spatial coherence by surface plasmons
We report on a method to generate a stationary interference pattern from two independent optical sources, each illuminating a single slit in Young's interference experiment. The pattern arises as a result of the action of surface plasmons traveling between subwavelength slits milled in a metal film. The visibility of the interference pattern can be manipulated by tuning the wavelength of one of the optical sources. © 2007 Optical. Society of America
Topological Aspect of Knotted Vortex Filaments in Excitable Media
Scroll waves exist ubiquitously in three-dimensional excitable media. It's
rotation center can be regarded as a topological object called vortex filament.
In three-dimensional space, the vortex filaments usually form closed loops, and
even linked and knotted. In this letter, we give a rigorous topological
description of knotted vortex filaments. By using the -mapping
topological current theory, we rewrite the topological current form of the
charge density of vortex filaments and use this topological current we reveal
that the Hopf invariant of vortex filaments is just the sum of the linking and
self-linking numbers of the knotted vortex filaments. We think that the precise
expression of the Hopf invariant may imply a new topological constraint on
knotted vortex filaments.Comment: 4 pages, no figures, Accepted by Chin. Phys. Let
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