1,610 research outputs found
Wave Mechanics and General Relativity: A Rapprochement
Using exact solutions, we show that it is in principle possible to regard
waves and particles as representations of the same underlying geometry, thereby
resolving the problem of wave-particle duality
FLRW Universes from "Wave-Like" Cosmologies in 5D
We consider the evolution of a 4D-universe embedded in a five-dimensional
(bulk) world with a large extra dimension and a cosmological constant. The
cosmology in 5D possesses "wave-like" character in the sense that the metric
coefficients in the bulk are functions of the extra coordinate and time in a
way similar to a pulse or traveling wave propagating along the fifth dimension.
This assumption is motivated by some recent work presenting the big-bang as a
higher dimensional shock wave. We show that this assumption, together with an
equation of state for the effective matter quantities in 4D, allows Einstein's
equations to be fully integrated. We then recover the familiar FLRW universes,
on the four-dimensional hypersurfaces orthogonal to the extra dimension.
Regarding the extra dimension we find that it is {\em growing} in size if the
universe is speeding up its expansion. We also get an estimate for the relative
change of the extra dimension over time. This estimate could have important
observational implications, notably for the time variation of rest mass,
electric charge and the gravitational "constant". Our results extend previous
ones in the literature.Comment: Few comments added, references updated. To appear in Int. J. of Mod.
Phys.
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
Gauge-Dependent Cosmological "Constant"
When the cosmological constant of spacetime is derived from the 5D
induced-matter theory of gravity, we show that a simple gauge transformation
changes it to a variable measure of the vacuum which is infinite at the big
bang and decays to an astrophysically-acceptable value at late epochs. We
outline implications of this for cosmology and galaxy formation.Comment: 14 pages, no figures, expanded version to be published in Class.
Quantum Gra
Extra symmetry in the field equations in 5D with spatial spherical symmetry
We point out that the field equations in 5D, with spatial spherical symmetry,
possess an extra symmetry that leaves them invariant. This symmetry corresponds
to certain simultaneous interchange of coordinates and metric coefficients. As
a consequence a single solution in 5D can generate very different scenarios in
4D, ranging from static configurations to cosmological situations. A new
perspective emanates from our work. Namely, that different astrophysical and
cosmological scenarios in 4D might correspond to the same physics in 5D. We
present explicit examples that illustrate this point of view.Comment: Typos corrected. Accepted for publication in Classical and Quantum
Gravit
Null Geodesics in Five Dimensional Manifolds
We analyze a class of 5D non-compact warped-product spaces characterized by
metrics that depend on the extra coordinate via a conformal factor. Our model
is closely related to the so-called canonical coordinate gauge of Mashhoon et
al. We confirm that if the 5D manifold in our model is Ricci-flat, then there
is an induced cosmological constant in the 4D sub-manifold. We derive the
general form of the 5D Killing vectors and relate them to the 4D Killing
vectors of the embedded spacetime. We then study the 5D null geodesic paths and
show that the 4D part of the motion can be timelike -- that is, massless
particles in 5D can be massive in 4D. We find that if the null trajectories are
affinely parameterized in 5D, then the particle is subject to an anomalous
acceleration or fifth force. However, this force may be removed by
reparameterization, which brings the correct definition of the proper time into
question. Physical properties of the geodesics -- such as rest mass variations
induced by a variable cosmological ``constant'', constants of the motion and 5D
time-dilation effects -- are discussed and are shown to be open to experimental
or observational investigation.Comment: 19 pages, REVTeX, in press in Gen. Rel. Gra
Induced Matter and Particle Motion in Non-Compact Kaluza-Klein Gravity
We examine generalizations of the five-dimensional canonical metric by
including a dependence of the extra coordinate in the four-dimensional metric.
We discuss a more appropriate way to interpret the four-dimensional
energy-momentum tensor induced from the five-dimensional space-time and show it
can lead to quite different physical situations depending on the interpretation
chosen. Furthermore, we show that the assumption of five-dimensional null
trajectories in Kaluza-Klein gravity can correspond to either four-dimensional
massive or null trajectories when the path parameterization is chosen properly.
Retaining the extra-coordinate dependence in the metric, we show the
possibility of a cosmological variation in the rest masses of particles and a
consequent departure from four-dimensional geodesic motion by a geometric
force. In the examples given, we show that at late times it is possible for
particles traveling along 5D null geodesics to be in a frame consistent with
the induced matter scenario.Comment: 29 pages, accepted to GR
The Structure of the Big Bang from Higher-Dimensional Embeddings
We give relations for the embedding of spatially-flat
Friedmann-Robertson-Walker cosmological models of Einstein's theory in flat
manifolds of the type used in Kaluza-Klein theory. We present embedding
diagrams that depict different 4D universes as hypersurfaces in a higher
dimensional flat manifold. The morphology of the hypersurfaces is found to
depend on the equation of state of the matter. The hypersurfaces possess a
line-like curvature singularity infinitesimally close to the
3-surface, where is the time expired since the big bang. The family of
timelike comoving geodesics on any given hypersurface is found to have a
caustic on the singular line, which we conclude is the 5D position of the
point-like big bang.Comment: 11 pages, 5 figures, revtex4, accepted in Class. Quant. Gra
Submanifolds in five-dimensional pseudo-Euclidean spaces and four-dimensional FRW universes
Equations for submanifolds, which correspond to embeddings of the
four-dimensional FRW universes in five-dimensional pseudo-Euclidean spaces, are
presented in convenient form in general case. Several specific examples are
considered.Comment: 7 pages, LaTeX, the mathematical part of this paper is based on the
withdrawn preprint arXiv:1012.0320 [gr-qc
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