5,194 research outputs found
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
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
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
Efficient fiber-optical interface for nanophotonic devices
We demonstrate a method for efficient coupling of guided light from a single
mode optical fiber to nanophotonic devices. Our approach makes use of
single-sided conical tapered optical fibers that are evanescently coupled over
the last ~10 um to a nanophotonic waveguide. By means of adiabatic mode
transfer using a properly chosen taper, single-mode fiber-waveguide coupling
efficiencies as high as 97(1)% are achieved. Efficient coupling is obtained for
a wide range of device geometries which are either singly-clamped on a chip or
attached to the fiber, demonstrating a promising approach for integrated
nanophotonic circuits, quantum optical and nanoscale sensing applications.Comment: 7 pages, 4 figures, includes supplementary informatio
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
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
Anisotropic Brane Cosmology with Variable and
In this work, the cosmological implications of brane world scenario are
investigated when the gravitational coupling and the cosmological term
are not constant but rather there are time variation of them. From
observational point of view, these time variations are taken in the form
and . The behavior of scale
factors and different kinematical parameters are investigated for different
possible scenarios where the bulk cosmological constant can be
zero, positive or negative.Comment: RevTex, 7 figures, 16 page
Exact Solutions of Five Dimensional Anisotropic Cosmologies
We solve the five dimensional vacuum Einstein equations for several kinds of
anisotropic geometries. We consider metrics in which the spatial slices are
characterized as Bianchi types-II and V, and the scale factors are dependent
both on time and a non-compact fifth coordinate. We examine the behavior of the
solutions we find, noting for which parameters they exhibit contraction over
time of the fifth scale factor, leading naturally to dimensional reduction. We
explore these within the context of the induced matter model: a Kaluza-Klein
approach that associates the extra geometric terms due to the fifth coordinate
with contributions to the four dimensional stress-energy tensor.Comment: 11 page
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
Latent solitons, black strings, black branes, and equations of state in Kaluza-Klein models
In Kaluza-Klein models with an arbitrary number of toroidal internal spaces,
we investigate soliton solutions which describe the gravitational field of a
massive compact object. We single out the physically interesting solution
corresponding to a point-like mass. For the general solution we obtain
equations of state in the external and internal spaces. These equations
demonstrate that the point-like mass soliton has dust-like equations of state
in all spaces. We also obtain the PPN parameters, which give the possibility to
obtain the formulas for perihelion shift, deflection of light and time delay of
radar echoes. Additionally, the gravitational experiments lead to a strong
restriction on the parameter of the model: . The point-like mass solution contradicts this restriction. The
condition satisfies the experimental limitation and defines a new
class of solutions which are indistinguishable from general relativity. We call
such solutions latent solitons. Black strings and black branes belong to this
class. Moreover, the condition of stability of the internal spaces singles out
black strings/branes from the latent solitons and leads uniquely to the black
string/brane equations of state , in the internal spaces and
to the number of the external dimensions . The investigation of
multidimensional static spherically symmetric perfect fluid with dust-like
equation of state in the external space confirms the above results.Comment: 8 pages, Revtex4, no figures, minor changes adde
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