1,373 research outputs found
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
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
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
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
The extinction and dust-to-gas structure of the planetary nebula NGC 7009 observed with MUSE
The large field and wavelength range of MUSE is well suited to mapping
Galactic planetary nebulae (PN). The bright PN NGC 7009 was observed with MUSE
on the VLT during the Science Verification of the instrument in seeing of 0.6".
Emission line maps in hydrogen Balmer and Paschen lines were formed from
analysis of the MUSE cubes. The measured electron temperature and density from
the MUSE cube were employed to predict the theoretical hydrogen line ratios and
map the extinction distribution across the nebula. After correction for the
interstellar extinction to NGC 7009, the internal dust-to-gas ratio (A_V/N_H)
has been mapped for the first time in a PN. The extinction map of NGC 7009 has
considerable structure, broadly corresponding to the morphological features of
the nebula. A large-scale feature in the extinction map, consisting of a crest
and trough, occurs at the rim of the inner shell. The nature of this feature
was investigated and instrumental and physical causes considered; no convincing
mechanisms were identified to produce this feature, other than mass loss
variations in the earlier asymptotic giant branch phase. The dust-to-gas ratio
A_V/N_H increases from 0.7 times the interstellar value to >5 times from the
centre towards the periphery of the ionized nebula. The integrated A_V/N_H is
about 2 times the mean ISM value. It is demonstrated that extinction mapping
with MUSE provides a powerful tool for studying the distribution of PN internal
dust and the dust-to-gas ratio. (Abridged.)Comment: 10 pages, 7 figures. Accepted by A&
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 Behavior of Kasner Cosmologies with Induced Matter
We extend the induced matter model, previously applied to a variety of
isotropic cases, to a generalization of Bianchi type-I anisotropic cosmologies.
The induced matter model is a 5D Kaluza-Klein approach in which assumptions of
compactness are relaxed for the fifth coordinate, leading to extra geometric
terms. One interpretation of these extra terms is to identify them as an
``induced matter'' contribution to the stress-energy tensor. In similar spirit,
we construct a five dimensional metric in which the spatial slices possess
Bianchi type-I geometry. We find a set of solutions for the five dimensional
Einstein equations, and determine the pressure and density of induced matter.
We comment on the long-term dynamics of the model, showing that the assumption
of positive density leads to the contraction over time of the fifth scale
factor.Comment: 14 page
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