6,977 research outputs found
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
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
Equivalence Between Space-Time-Matter and Brane-World Theories
We study the relationship between space-time-matter (STM) and brane theories.
These two theories look very different at first sight, and have different
motivation for the introduction of a large extra dimension. However, we show
that they are equivalent to each other. First we demonstrate that STM predicts
local and non-local high-energy corrections to general relativity in 4D, which
are identical to those predicted by brane-world models. Secondly, we notice
that in brane models the usual matter in 4D is a consequence of the dependence
of five-dimensional metrics on the extra coordinate. If the 5D bulk metric is
independent of the extra dimension, then the brane is void of matter. Thus, in
brane theory matter and geometry are unified, which is exactly the paradigm
proposed in STM. Consequently, these two 5D theories share the same concepts
and predict the same physics. This is important not only from a theoretical
point of view, but also in practice. We propose to use a combination of both
methods to alleviate the difficult task of finding solutions on the brane. We
show an explicit example that illustrate the feasibility of our proposal.Comment: Typos corrected, three references added. To appear in Mod. Phys. Let
Mass and Charge in Brane-World and Non-Compact Kaluza-Klein Theories in 5 Dim
In classical Kaluza-Klein theory, with compactified extra dimensions and
without scalar field, the rest mass as well as the electric charge of test
particles are constants of motion. We show that in the case of a large extra
dimension this is no longer so. We propose the Hamilton-Jacobi formalism,
instead of the geodesic equation, for the study of test particles moving in a
five-dimensional background metric. This formalism has a number of advantages:
(i) it provides a clear and invariant definition of rest mass, without the
ambiguities associated with the choice of the parameters used along the motion
in 5D and 4D, (ii) the electromagnetic field can be easily incorporated in the
discussion, and (iii) we avoid the difficulties associated with the "splitting"
of the geodesic equation. For particles moving in a general 5D metric, we show
how the effective rest mass, as measured by an observer in 4D, varies as a
consequence of the large extra dimension. Also, the fifth component of the
momentum changes along the motion. This component can be identified with the
electric charge of test particles. With this interpretation, both the rest mass
and the charge vary along the trajectory. The constant of motion is now a
combination of these quantities. We study the cosmological variations of charge
and rest mass in a five-dimensional bulk metric which is used to embed the
standard k = 0 FRW universes. The time variations in the fine structure
"constant" and the Thomson cross section are also discussed.Comment: V2: References added, discussion extended. V3 is identical to V2,
references updated. To appear in General Relativity and Gravitatio
The Effective Energy-Momentum Tensor in Kaluza-Klein Gravity With Large Extra Dimensions and Off-Diagonal Metrics
We consider a version of Kaluza-Klein theory where the cylinder condition is
not imposed. The metric is allowed to have explicit dependence on the "extra"
coordinate(s). This is the usual scenario in brane-world and space-time-matter
theories. We extend the usual discussion by considering five-dimensional
metrics with off-diagonal terms. We replace the condition of cylindricity by
the requirement that physics in four-dimensional space-time should remain
invariant under changes of coordinates in the five-dimensional bulk. This
invariance does not eliminate physical effects from the extra dimension but
separates them from spurious geometrical ones. We use the appropriate splitting
technique to construct the most general induced energy-momentum tensor,
compatible with the required invariance. It generalizes all previous results in
the literature. In addition, we find two four-vectors, J_{m}^{mu} and
J_{e}^{mu}, induced by off-diagonal metrics, that separately satisfy the usual
equation of continuity in 4D. These vectors appear as source-terms in equations
that closely resemble the ones of electromagnetism. These are Maxwell-like
equations for an antisymmetric tensor {F-hat}_{mu nu} that generalizes the
usual electromagnetic one. This generalization is not an assumption, but
follows naturally from the dimensional reduction. Thus, if {F-hat}_{mu nu}
could be identified with the electromagnetic tensor, then the theory would
predict the existence of classical magnetic charge and current. The splitting
formalism used allows us to construct 4D physical quantities from
five-dimensional ones, in a way that is independent on how we choose our
space-time coordinates from those of the bulk.Comment: New title, editorial changes made as to match the version to appear
in International Journal of Modern Physics
Low frequency interference between short synchrotron radiation sources
A recently developed analytical formalism describing low frequency far-field synchrotron radiation (SR) is applied to the calculation of spectral angular radiation densities from interfering short sources (edge, short magnet). This is illustrated by analytical calculation of synchrotron radiation from various assemblies of short dipoles, including an âisolatedâ highest density infrared SR source
Late time cosmic acceleration from vacuum Brans-Dicke theory in 5D
We show that the scalar-vacuum Brans-Dicke equations in 5D are equivalent to
Brans-Dicke theory in 4D with a self interacting potential and an effective
matter field. The cosmological implication, in the context of FRW models, is
that the observed accelerated expansion of the universe comes naturally from
the condition that the scalar field is not a ghost, i.e., . We
find an effective matter-dominated 4D universe which shows accelerated
expansion if . We study the question of whether
accelerated expansion can be made compatible with large values of ,
within the framework of a 5D scalar-vacuum Brans-Dicke theory with variable,
instead of constant, parameter . In this framework, and based on a
general class of solutions of the field equations, we demonstrate that
accelerated expansion is incompatible with large values of .Comment: In V2 the summary section is expanded. To be published in Classical
and Quantum Gravity
From Traditional to Modern : Domain Adaptation for Action Classification in Short Social Video Clips
Short internet video clips like vines present a significantly wild
distribution compared to traditional video datasets. In this paper, we focus on
the problem of unsupervised action classification in wild vines using
traditional labeled datasets. To this end, we use a data augmentation based
simple domain adaptation strategy. We utilise semantic word2vec space as a
common subspace to embed video features from both, labeled source domain and
unlablled target domain. Our method incrementally augments the labeled source
with target samples and iteratively modifies the embedding function to bring
the source and target distributions together. Additionally, we utilise a
multi-modal representation that incorporates noisy semantic information
available in form of hash-tags. We show the effectiveness of this simple
adaptation technique on a test set of vines and achieve notable improvements in
performance.Comment: 9 pages, GCPR, 201
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