9,094 research outputs found
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It is well-known that Birkhoff's theorem is no longer valid in theories with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
The Impact of a Cash Transfer Program on Cognitive Achievement: The Bono de Desarrollo Humano of Ecuador
Throughout Latin America, conditional cash transfer (CCT) programs play an important role in social policy. These programs aim to influence the accumulation of human capital, as well as reduce poverty. In terms of educational outcomes, a number of impact evaluation studies have shown that such programs have led to an increase in school enrollment, ensured regular school attendance and led to a reduction in child labor. Theoretically, such cash transfer programs may also be expected to exert a positive impact on students’ test scores, but related empirical evidence is scarce. Accordingly, this paper evaluates the impact of a cash transfer program, the Bono de Desarrollo Humano of Ecuador, on students’ cognitive achievements. The paper uses a regression discontinuity strategy to identify the impact of the program on second grade cognitive achievement. Regardless of the specification and the sample used, we find that there is no impact of the program on test scores, suggesting that attempts at building human capital, as measured by cognitive achievement, require additional and alternative interventions.cash transfers, test scores, regression discontinuity
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
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
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
Brane classical and quantum cosmology from an effective action
Motivated by the Randall-Sundrum brane-world scenario, we discuss the
classical and quantum dynamics of a (d+1)-dimensional boundary wall between a
pair of (d+2)-dimensional topological Schwarzschild-AdS black holes. We assume
there are quite general -- but not completely arbitrary -- matter fields living
on the boundary ``brane universe'' and its geometry is that of an
Friedmann-Lemaitre-Robertson-Walker (FLRW) model. The effective action
governing the model in the mini-superspace approximation is derived. We find
that the presence of black hole horizons in the bulk gives rise to a complex
action for certain classically allowed brane configurations, but that the
imaginary contribution plays no role in the equations of motion. Classical and
instanton brane trajectories are examined in general and for special cases, and
we find a subset of configuration space that is not allowed at the classical or
semi-classical level; these correspond to spacelike branes carrying tachyonic
matter. The Hamiltonization and Dirac quantization of the model is then
performed for the general case; the latter involves the manipulation of the
Hamiltonian constraint before it is transformed into an operator that
annihilates physical state vectors. The ensuing covariant Wheeler-DeWitt
equation is examined at the semi-classical level, and we consider the possible
localization of the brane universe's wavefunction away from the cosmological
singularity. This is easier to achieve for branes with low density and/or
spherical spatial sections.Comment: Shortened to match version accepted by Phys. Rev. D (unabridged text
found in version 2), 42 pages, 9 figures, Rextex
Kaluza-Klein solitons reexamined
In (4 + 1) gravity the assumption that the five-dimensional metric is
independent of the fifth coordinate authorizes the extra dimension to be either
spacelike or timelike. As a consequence of this, the time coordinate and the
extra coordinate are interchangeable, which in turn allows the conception of
different scenarios in 4D from a single solution in 5D. In this paper, we make
a thorough investigation of all possible 4D scenarios, associated with this
interchange, for the well-known Kramer-Gross-Perry-Davidson-Owen set of
solutions. We show that there are {\it three} families of solutions with very
distinct geometrical and physical properties. They correspond to different sets
of values of the parameters which characterize the solutions in 5D. The
solutions of physical interest are identified on the basis of physical
requirements on the induced-matter in 4D. We find that only one family
satisfies these requirements; the other two violate the positivity of
mass-energy density. The "physical" solutions possess a lightlike singularity
which coincides with the horizon. The Schwarzschild black string solution as
well as the zero moment dipole solution of Gross and Perry are obtained in
different limits. These are analyzed in the context of Lake's geometrical
approach. We demonstrate that the parameters of the solutions in 5D are not
free, as previously considered. Instead, they are totally determined by
measurements in 4D. Namely, by the surface gravitational potential of the
astrophysical phenomena, like the Sun or other stars, modeled in Kaluza-Klein
theory. This is an important result which may help in observations for an
experimental/observational test of the theory.Comment: In V2 we include an Appendix, where we examine the conformal
approach. Minor changes at the beginning of section 2. In V3 more references
are added. Minor editorial changes in the Introduction and Conclusions
section
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
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