815 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
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
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withdrawn preprint arXiv:1012.0320 [gr-qc
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
Static Ricci-flat 5-manifolds admitting the 2-sphere
We examine, in a purely geometrical way, static Ricci-flat 5-manifolds
admitting the 2-sphere and an additional hypersurface-orthogonal Killing
vector. These are widely studied in the literature, from different physical
approaches, and known variously as the Kramer - Gross - Perry - Davidson - Owen
solutions. The 2-fold infinity of cases that result are studied by way of new
coordinates (which are in most cases global) and the cases likely to be of
interest in any physical approach are distinguished on the basis of the
nakedness and geometrical mass of their associated singularities. It is argued
that the entire class of solutions has to be considered unstable about the
exceptional solutions: the black string and soliton cases. Any physical theory
which admits the non-exceptional solutions as the external vacuua of a
collapsing object has to accept the possibility of collapse to zero volume
leaving behind the weakest possible, albeit naked, geometrical singularities at
the origin.Finally, it is pointed out that these types of solutions generalize,
in a straightforward way, to higher dimensions.Comment: Generalize, in a straightforward way, to higher dimension
Early evolution of electron cyclotron driven current during suppression of tearing modes in a circular tokamak
When electron cyclotron (EC) driven current is first applied to the inside of
a magnetic island, the current spreads throughout the island and after a short
period achieves a steady level. Using a two equation fluid model for the EC
current that allows us to examine this early evolution in detail, we analyze
high-resolution simulations of a 2/1 classical tearing mode in a low-beta large
aspect-ratio circular tokamak. These simulations use a nonlinear 3D reduced-MHD
fluid model and the JOREK code. During the initial period where the EC driven
current grows and spreads throughout the magnetic island, it is not a function
of the magnetic flux. However, once it has reached a steady-state, it should be
a flux function. We demonstrate numerically that if sufficiently resolved
toroidally, the steady-state EC driven current becomes approximately a flux
function. We discuss the physics of this early period of EC evolution and its
impact on the size of the magnetic island.Comment: 12 pages, 7 figure
Causal Anomalies in Kaluza-Klein Gravity Theories
Causal anomalies in two Kaluza-Klein gravity theories are examined,
particularly as to whether these theories permit solutions in which the
causality principle is violated. It is found that similarly to general
relativity the field equations of the space-time-mass Kaluza-Klein (STM-KK)
gravity theory do not exclude violation of causality of G\"odel type, whereas
the induced matter Kaluza-Klein (IM-KK) gravity rules out noncausal
G\"odel-type models. The induced matter version of general relativity is shown
to be an efficient therapy for causal anomalies that occurs in a wide class of
noncausal geometries. Perfect fluid and dust G\"odel-type solutions of the
STM-KK field equations are studied. It is shown that every G\"odel-type perfect
fluid solution is isometric to the unique dust solution of the STM-KK field
equations. The question as to whether 5-D G\"odel-type non-causal geometries
induce any physically acceptable 4-D energy-momentum tensor is also addressed.Comment: 16 page. LaTex file. To appear in Int. J. Mod. Phys. A (1998
Modern cosmologies from empty Kaluza-Klein solutions in 5D
We show that the empty five-dimensional solutions of
Davidson-Sonnenschtein-Vozmediano, {\em Phys. Rev.} {\bf D32} (1985)1330, in
the "old" Kaluza-Klein gravity, under appropriate interpretation can generate
an ample variety of cosmological models in 4D, which include the
higher-dimensional modifications to general relativity predicted by "modern"
versions of noncompactified 5D gravity as, e.g., induced-matter and braneworld
theories. This is the first time that these solutions are investigated in a
systematic way as embeddings for cosmological models in 4D. They provide a
different formulation, which is complementary to the approaches used in current
versions of 5D relativity.Comment: Accepted for publication in JHE
A Class of Anisotropic Five-Dimensional Solutions for the Early Universe
We solve the Ricci-flat equations of extended general relativity to obtain an
interesting class of cosmological models. The solutions are analogous to the 4D
ones of Bianchi type-I of Kasner type and have significant implications for
astrophysics.Comment: V2 has some minor editorial changes in the introductio
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
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