226 research outputs found
Rydberg states of hydrogen-like ions in braneworld
It has been argued that precise measurements of optical transition
frequencies between Rydberg states of hydrogen-like ions could be used to
obtain an improved value of the Rydberg constant and even to test Quantum
Electrodynamics (QED) theory more accurately, by avoiding the uncertainties
about the proton radius. Motivated by this perspective, we investigate the
influence of the gravitational interaction on the energy levels of
Hydrogen-like ions in Rydberg states within the context of the braneworld
models. As it is known, in this scenario, the gravitational interaction is
amplified in short distances. We show that, for Rydberg states, the main
contribution for the gravitational potential energy does not come from the rest
energy concentrated on the nucleus but from the energy of the electromagnetic
field created by its electrical charge, which is spread in space. The reason is
connected to the fact that, when the ion is in a Rydberg state with high
angular momentum, the gravitational potential energy is not computable in
zero-width brane approximation due to the gravitational influence of the
electrovacuum in which the lepton is moving. Considering a thick brane
scenario, we calculate the gravitational potential energy associated to the
nucleus charge in terms of the confinement parameter of the electric field in
the brane. We show that the gravitational effects on the energy levels of a
Rydberg state can be amplified by the extra dimensions even when the
compactification scale of the hidden dimensions is shorter than the Bohr
radius
Inducing the cosmological constant from five-dimensional Weyl space
We investigate the possibility of inducing the cosmological constant from
extra dimensions by embedding our four-dimensional Riemannian space-time into a
five-dimensional Weyl integrable space. Following approach of the induced
matter theory we show that when we go down from five to four dimensions, the
Weyl field may contribute both to the induced energy-tensor as well as to the
cosmological constant, or more generally, it may generate a time-dependent
cosmological parameter. As an application, we construct a simple cosmological
model which has some interesting properties.Comment: 7 page
The embedding of the spacetime in five dimensions: an extension of Campbell-Magaard theorem
We extend Campbell-Magaard embedding theorem by proving that any
n-dimensional semi-Riemannian manifold can be locally embedded in an
(n+1)-dimensional Einstein space. We work out some examples of application of
the theorem and discuss its relevance in the context of modern
higher-dimensional spacetime theories.Comment: 22pages, Revte
Ideally embedded space-times
Due to the growing interest in embeddings of space-time in higher-dimensional
spaces we consider a specific type of embedding. After proving an inequality
between intrinsically defined curvature invariants and the squared mean
curvature, we extend the notion of ideal embeddings from Riemannian geometry to
the indefinite case. Ideal embeddings are such that the embedded manifold
receives the least amount of tension from the surrounding space. Then it is
shown that the de Sitter spaces, a Robertson-Walker space-time and some
anisotropic perfect fluid metrics can be ideally embedded in a five-dimensional
pseudo-Euclidean space.Comment: layout changed and typos corrected; uses revtex
Embeddings in Spacetimes Sourced by Scalar Fields
The extension of the Campbell-Magaard embedding theorem to general relativity
with minimally-coupled scalar fields is formulated and proven. The result is
applied to the case of a self-interacting scalar field for which new embeddings
are found, and to Brans-Dicke theory. The relationship between Campbell-Magaard
theorem and the general relativity, Cauchy and initial value problems is
outlined.Comment: RevTEX (11 pages)/ To appear in the Journal of Mathematical Physic
Inducing charges and currents from extra dimensions
In a particular variant of Kaluza-Klein theory, the so-called induced-matter
theory (IMT), it is shown that any configuration of matter may be geometrically
induced from a five-dimensional vacuum space. By using a similar approach we
show that any distribution of charges and currents may also be induced from a
five-dimensional vacuum space. Whereas in the case of IMT the geometry is
Riemannian and the fundamental equations are the five-dimensional Einstein
equations in vacuum, here we consider a Minkowskian geometry and the
five-dimensional Maxwell equations in vacuum.Comment: 8 pages. Accepted for publication in Modern Physics Letters
Banach-Steinhaus theorem for linear relations on asymmetric normed spaces
We study the continuity of linear relations defined on asymmetric normed spaces with values in normed spaces. We give some geometric charactirization of these mappings. As an application, we prove the Banach-Steinhaus theorem in the framework of asymmetric normed spaces
On the embedding of branes in five-dimensional spaces
We investigate the embedding of four-dimensional branes in five-dimensional
spaces. We firstly consider the case when the embedding space is a vacuum bulk
whose energy-momentum tensor consists of a Dirac delta function with support in
the brane. We then consider the embedding in the context of
Randall-Sundrum-type models, taking into account symmetry and a
cosmological constant. We employ the Campbell-Magaard theorem to construct the
embeddings and are led to the conclusion that the content of energy-matter of
the brane does not necessarily determine its curvature. Finally, as an
application to illustrate our results, we construct the embedding of Minkowski
spacetime filled with dust.Comment: 12 pages - REVTEX To appear in Classical and Quantum Gravit
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