8,723 research outputs found
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
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
Exterior spacetime for stellar models in 5-dimensional Kaluza-Klein gravity
It is well-known that Birkhoff's theorem is no longer valid in theories with
more than four dimensions. Thus, in these theories the effective 4-dimensional
picture allows the existence of different possible, non-Schwarzschild,
scenarios for the description of the spacetime outside of a spherical star,
contrary to general relativity in 4D. We investigate the exterior spacetime of
a spherically symmetric star in the context of Kaluza-Klein gravity. We take a
well-known family of static spherically symmetric solutions of the Einstein
equations in an empty five-dimensional universe, and analyze possible stellar
exteriors that are conformal to the metric induced on four-dimensional
hypersurfaces orthogonal to the extra dimension. All these exteriors are
continuously matched with the interior of the star. Then, without making any
assumptions about the interior solution, we prove the following statement: the
condition that in the weak-field limit we recover the usual Newtonian physics
singles out an unique exterior. This exterior is "similar" to Scharzschild
vacuum in the sense that it has no effect on gravitational interactions.
However, it is more realistic because instead of being absolutely empty, it is
consistent with the existence of quantum zero-point fields. We also examine the
question of how would the deviation from the Schwarzschild vacuum exterior
affect the parameters of a neutron star. In the context of a model star of
uniform density, we show that the general relativity upper limit M/R < 4/9 is
significantly increased as we go away from the Schwarzschild vacuum exterior.
We find that, in principle, the compactness limit of a star can be larger than
1/2, without being a black hole. The generality of our approach is also
discussed.Comment: Typos corrected. Accepted for publication in Classical and Quantum
Gravit
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
An analytic model for the transition from decelerated to accelerated cosmic expansion
We consider the scenario where our observable universe is devised as a
dynamical four-dimensional hypersurface embedded in a five-dimensional bulk
spacetime, with a large extra dimension, which is the {\it generalization of
the flat FRW cosmological metric to five dimensions}. This scenario generates a
simple analytical model where different stages of the evolution of the universe
are approximated by distinct parameterizations of the {\it same} spacetime. In
this model the evolution from decelerated to accelerated expansion can be
interpreted as a "first-order" phase transition between two successive stages.
The dominant energy condition allows different parts of the universe to evolve,
from deceleration to acceleration, at different redshifts within a narrow era.
This picture corresponds to the creation of bubbles of new phase, in the middle
of the old one, typical of first-order phase transitions. Taking today, we find that the cross-over from deceleration to acceleration
occurs at , regardless of the equation of state in the very
early universe. In the case of primordial radiation, the model predicts that
the deceleration parameter "jumps" from to at . At the present time and the equation of state of the
universe is , in agreement with observations and some
theoretical predictions.Comment: The abstract and introduction are improved and the discussion section
is expanded. A number of references are adde
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
How can aviation law and policy facilitate open access to the new airport of Istanbul
Dr. Mendes de Leon as legal professor and expert in aviation touched on several legal aspects that Turkey’s airports, airlines and authorities could think when preparing for the opening of the new airport.Dr. Mendes de Leon, Hukuk profesörü ve Havacılık alanında bir uzman olarak, Türkiye’nin havaalanlarının, havayollarının ve otoriterinin, yeni bir havaalanı açmaya hazırlandıklarında düşünebilecekleri bir kaç yasal açıya değindi
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