6,975 research outputs found
Self-similar cosmologies in 5D: spatially flat anisotropic models
In the context of theories of Kaluza-Klein type, with a large extra
dimension, we study self-similar cosmological models in 5D that are
homogeneous, anisotropic and spatially flat. The "ladder" to go between the
physics in 5D and 4D is provided by Campbell-Maagard's embedding theorems. We
show that the 5-dimensional field equations determine the form of
the similarity variable. There are three different possibilities: homothetic,
conformal and "wave-like" solutions in 5D. We derive the most general
homothetic and conformal solutions to the 5D field equations. They require the
extra dimension to be spacelike, and are given in terms of one arbitrary
function of the similarity variable and three parameters. The Riemann tensor in
5D is not zero, except in the isotropic limit, which corresponds to the case
where the parameters are equal to each other. The solutions can be used as 5D
embeddings for a great variety of 4D homogeneous cosmological models, with and
without matter, including the Kasner universe. Since the extra dimension is
spacelike, the 5D solutions are invariant under the exchange of spatial
coordinates. Therefore they also embed a family of spatially {\it
inhomogeneous} models in 4D. We show that these models can be interpreted as
vacuum solutions in braneworld theory. Our work (I) generalizes the 5D
embeddings used for the FLRW models; (II) shows that anisotropic cosmologies
are, in general, curved in 5D, in contrast with FLRW models which can always be
embedded in a 5D Riemann-flat (Minkowski) manifold; (III) reveals that
anisotropic cosmologies can be curved and devoid of matter, both in 5D and 4D,
even when the metric in 5D explicitly depends on the extra coordinate, which is
quite different from the isotropic case.Comment: Typos corrected. Minor editorial changes and additions in the
Introduction and Summary section
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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
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
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Brane world solutions of perfect fluid in the background of a bulk containing dust or cosmological constant
The paper presents some solutions to the five dimensional Einstein equations
due to a perfect fluid on the brane with pure dust filling the entire bulk in
one case and a cosmological constant (or vacuum) in the bulk for the second
case. In the first case, there is a linear relationship between isotropic
pressure, energy density and the brane tension, while in the second case, the
perfect fluid is assumed to be in the form of chaplygin gas. Cosmological
solutions are found both for brane and bulk scenarios and some interesting
features are obtained for the chaplygin gas on the brane which are distinctly
different from the standard cosmology in four dimensions.Comment: 10 Latex pages, 5 figure
Wave-like Solutions for Bianchi type-I cosmologies in 5D
We derive exact solutions to the vacuum Einstein field equations in 5D, under
the assumption that (i) the line element in 5D possesses self-similar symmetry,
in the classical understanding of Sedov, Taub and Zeldovich, and that (ii) the
metric tensor is diagonal and independent of the coordinates for ordinary 3D
space. These assumptions lead to three different types of self-similarity in
5D: homothetic, conformal and "wave-like". In this work we present the most
general wave-like solutions to the 5D field equations. Using the standard
technique based on Campbell's theorem, they generate a large number of
anisotropic cosmological models of Bianchi type-I, which can be applied to our
universe after the big-bang, when anisotropies could have played an important
role. We present a complete review of all possible cases of self-similar
anisotropic cosmologies in 5D. Our analysis extends a number of previous
studies on wave-like solutions in 5D with spatial spherical symmetry
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
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
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
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