1,154 research outputs found
Classical and quantized aspects of dynamics in five dimensional relativity
A null path in 5D can appear as a timelike path in 4D, and for a certain
gauge in 5D the motion of a massive particle in 4D obeys the usual quantization
rule with an uncertainty-type relation. Generalizations of this result are
discussed in regard to induced-matter and membrane theory.Comment: 26 pages, in press in Class. Quant. Gra
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.
Quantum cosmology of 5D non-compactified Kaluza-Klein theory
We study the quantum cosmology of a five dimensional non-compactified
Kaluza-Klein theory where the 4D metric depends on the fifth coordinate,
. This model is effectively equivalent to a 4D non-minimally
coupled dilaton field in addition to matter generated on hypersurfaces
l=constant by the extra coordinate dependence in the four-dimensional metric.
We show that the Vilenkin wave function of the universe is more convenient for
this model as it predicts a new-born 4D universe on the constant
hypersurface.Comment: 14 pages, LaTe
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
An exact solution of the five-dimensional Einstein equations with four-dimensional de Sitter-like expansion
We present an exact solution to the Einstein field equations which is Ricci
and Riemann flat in five dimensions, but in four dimensions is a good model for
the early vacuum-dominated universe.Comment: 6 pages; to appear in Journal of Mathematical Physics; v2: reference
3 correcte
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
Cosmological Implications of a Non-Separable 5D Solution of the Vacuum Einstein Field Equations
An exact class of solutions of the 5D vacuum Einstein field equations (EFEs)
is obtained. The metric coefficients are found to be non-separable functions of
time and the extra coordinate and the induced metric on = constant
hypersurfaces has the form of a Friedmann-Robertson-Walker cosmology. The 5D
manifold and 3D and 4D submanifolds are in general curved, which distinguishes
this solution from previous ones in the literature. The singularity structure
of the manifold is explored: some models in the class do not exhibit a big
bang, while other exhibit a big bang and a big crunch. For the models with an
initial singularity, the equation of state of the induced matter evolves from
radiation like at early epochs to Milne-like at late times and the big bang
manifests itself as a singular hypersurface in 5D. The projection of comoving
5D null geodesics onto the 4D submanifold is shown to be compatible with
standard 4D comoving trajectories, while the expansion of 5D null congruences
is shown to be in line with conventional notions of the Hubble expansion.Comment: 8 pages, in press in J. Math. Phy
Stabilization of test particles in Induced Matter Kaluza-Klein theory
The stability conditions for the motion of classical test particles in an -dimensional Induced Matter Kaluza-Klein theory is studied. We show that
stabilization requires a variance of the strong energy condition for the
induced matter to hold and that it is related to the hierarchy problem.
Stabilization of test particles in a FRW universe is also discussed.Comment: 15 pages, 1 figure, to appear in Class. Quantum 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
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