9,796 research outputs found
A new geometric setting for classical field theories
A new geometrical setting for classical field theories is introduced. This
description is strongly inspired in the one due to Skinner and Rusk for
singular lagrangians systems. For a singular field theory a constraint
algorithm is developed that gives a final constraint submanifold where a
well-defined dynamics exists. The main advantage of this algorithm is that the
second order condition is automatically included.Comment: 22 page
Hydrostatic Equilibrium of a Perfect Fluid Sphere with Exterior Higher-Dimensional Schwarzschild Spacetime
We discuss the question of how the number of dimensions of space and time can
influence the equilibrium configurations of stars. We find that dimensionality
does increase the effect of mass but not the contribution of the pressure,
which is the same in any dimension. In the presence of a (positive)
cosmological constant the condition of hydrostatic equilibrium imposes a lower
limit on mass and matter density. We show how this limit depends on the number
of dimensions and suggest that is more effective in 4D than in
higher dimensions. We obtain a general limit for the degree of compactification
(gravitational potential on the boundary) of perfect fluid stars in
-dimensions. We argue that the effects of gravity are stronger in 4D than in
any other number of dimensions. The generality of the results is also
discussed
Leibniz algebroid associated with a Nambu-Poisson structure
The notion of Leibniz algebroid is introduced, and it is shown that each
Nambu-Poisson manifold has associated a canonical Leibniz algebroid. This fact
permits to define the modular class of a Nambu-Poisson manifold as an
appropiate cohomology class, extending the well-known modular class of Poisson
manifolds
Stellar models with Schwarzschild and non-Schwarzschild vacuum exteriors
A striking characteristic of non-Schwarzschild vacuum exteriors is that they
contain not only the total gravitational mass of the source, but also an {\it
arbitrary} constant. In this work, we show that the constants appearing in the
"temporal Schwarzschild", "spatial Schwarzschild" and
"Reissner-Nordstr{\"o}m-like" exteriors are not arbitrary but are completely
determined by star's parameters, like the equation of state and the
gravitational potential. Consequently, in the braneworld scenario the
gravitational field outside of a star is no longer determined by the total mass
alone, but also depends on the details of the internal structure of the source.
We show that the general relativistic upper bound on the gravitational
potential , for perfect fluid stars, is significantly increased in
these exteriors. Namely, , and for the
temporal Schwarzschild, spatial Schwarzschild and Reissner-Nordstr{\"o}m-like
exteriors, respectively. Regarding the surface gravitational redshift, we find
that the general relativistic Schwarzschild exterior as well as the braneworld
spatial Schwarzschild exterior lead to the same upper bound, viz., .
However, when the external spacetime is the temporal Schwarzschild metric or
the Reissner-Nordstr{\"o}m-like exterior there is no such constraint: . This infinite difference in the limiting value of is because for
these exteriors the effective pressure at the surface is negative. The results
of our work are potentially observable and can be used to test the theory.Comment: 19 pages, 3 figures and caption
Comparison of the Refractive Index Structure Constant Derived from Numerical Weather Prediction (NWP) Models and Thermosonde Data
An accurate depiction of atmospheric turbulence is required for successful employment of a viable airborne laser for the Department of Defense (DOD). The ABL Special Program Office (SEC) which is tasked by the Missile Defense Agency (MDA) bas not designated any particular numerical weather model that is tasked exclusively to model optical turbulence This research compares CLEAR1, 2 X CLEAR I and thermosonde derived values of the refractive index structure constant to optical turbulence values derived from several numerical weather prediction models currently in use by the DOD. The models used were the fifth Generation Mesoscale Model (MM5), the Coupled Ocean Atmosphere Prediction System (COAMPS) and the Advanced Climate Modeling and Environmental Simulation (ACMES) program Comparisons are presented using thermosonde data collected at Vandenberg AEB California during the period l9-26 Oct 200l Universal Time Coordinated (UTC ) Results indicate that the model-derived optical turbulence and the thermosonde derived optical turbulence values are statistically different in many case
Extended Hamiltonian systems in multisymplectic field theories
We consider Hamiltonian systems in first-order multisymplectic field
theories. We review the properties of Hamiltonian systems in the so-called
restricted multimomentum bundle, including the variational principle which
leads to the Hamiltonian field equations. In an analogous way to how these
systems are defined in the so-called extended (symplectic) formulation of
non-autonomous mechanics, we introduce Hamiltonian systems in the extended
multimomentum bundle. The geometric properties of these systems are studied,
the Hamiltonian equations are analyzed using integrable multivector fields, the
corresponding variational principle is also stated, and the relation between
the extended and the restricted Hamiltonian systems is established. All these
properties are also adapted to certain kinds of submanifolds of the
multimomentum bundles in order to cover the case of almost-regular field
theories.Comment: 36 pp. The introduction and the abstract have been rewritten. New
references are added and some little mistakes are corrected. The title has
been slightly modifie
Transition from decelerated to accelerated cosmic expansion in braneworld universes
Braneworld theory provides a natural setting to treat, at a classical level,
the cosmological effects of vacuum energy. Non-static extra dimensions can
generally lead to a variable vacuum energy, which in turn may explain the
present accelerated cosmic expansion. We concentrate our attention in models
where the vacuum energy decreases as an inverse power law of the scale factor.
These models agree with the observed accelerating universe, while fitting
simultaneously the observational data for the density and deceleration
parameter. The redshift at which the vacuum energy can start to dominate
depends on the mass density of ordinary matter. For Omega = 0.3, the transition
from decelerated to accelerated cosmic expansion occurs at z approx 0.48 +/-
0.20, which is compatible with SNe data. We set a lower bound on the
deceleration parameter today, namely q > - 1 + 3 Omega/2, i.e., q > - 0.55 for
Omega = 0.3. The future evolution of the universe crucially depends on the time
when vacuum starts to dominate over ordinary matter. If it dominates only
recently, at an epoch z < 0.64, then the universe is accelerating today and
will continue that way forever. If vacuum dominates earlier, at z > 0.64, then
the deceleration comes back and the universe recollapses at some point in the
distant future. In the first case, quintessence and Cardassian expansion can be
formally interpreted as the low energy limit of our model, although they are
entirely different in philosophy. In the second case there is no correspondence
between these models and ours.Comment: In V2 typos are corrected and one reference is added for section 1.
To appear in General Relativity and Gravitatio
Accelerated expansion from braneworld models with variable vacuum energy
In braneworld models a variable vacuum energy may appear if the size of the
extra dimension changes during the evolution of the universe. In this scenario
the acceleration of the universe is related not only to the variation of the
cosmological term, but also to the time evolution of and, possibly, to the
variation of other fundamental "constants" as well. This is because the
expansion rate of the extra dimension appears in different contexts, notably in
expressions concerning the variation of rest mass and electric charge. We
concentrate our attention on spatially-flat, homogeneous and isotropic,
brane-universes where the matter density decreases as an inverse power of the
scale factor, similar (but at different rate) to the power law in FRW-universes
of general relativity.
We show that these braneworld cosmologies are consistent with the observed
accelerating universe and other observational requirements. In particular,
becomes constant and asymptotically in
time. Another important feature is that the models contain no "adjustable"
parameters. All the quantities, even the five-dimensional ones, can be
evaluated by means of measurements in 4D. We provide precise constrains on the
cosmological parameters and demonstrate that the "effective" equation of state
of the universe can, in principle, be determined by measurements of the
deceleration parameter alone. We give an explicit expression relating the
density parameters , and the deceleration
parameter . These results constitute concrete predictions that may help in
observations for an experimental/observational test of the model.Comment: References added, typos correcte
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