29 research outputs found
Wesson's IMT with a Weylian bulk
The foundations of Wesson's induced matter theory are analyzed. It is shown
that the 5D empty bulk must be regarded rather as a Weylian space than as a
Riemannian one.The framework of a Weyl-Dirac version of Wesson's theory is
elaborated and discussed. The bulk possesses in addition to the metric tensor a
Weylian connection vector as well Dirac's gauge function; there are no sources
(mass, current) in the bulk. On the 4D brane one obtains a geometrically based
unified theory of gravitation and electromagnetism with mass, currents and
equations induced by the 5D bulkComment: 29 page
Classical confinement of test particles in higher-dimensional models: stability criteria and a new energy condition
We review the circumstances under which test particles can be localized
around a spacetime section \Sigma_0 smoothly contained within a codimension-1
embedding space M. If such a confinement is possible, \Sigma_0 is said to be
totally geodesic. Using three different methods, we derive a stability
condition for trapped test particles in terms of intrinsic geometrical
quantities on \Sigma_0 and M; namely, confined paths are stable against
perturbations if the gravitational stress-energy density on M is larger than
that on \Sigma_0, as measured by an observed travelling along the unperturbed
trajectory. We confirm our general result explicitly in two different cases:
the warped-product metric ansatz for (n+1)-dimensional Einstein spaces, and a
known solution of the 5-dimensional vacuum field equation embedding certain
4-dimensional cosmologies. We conclude by defining a confinement energy
condition that can be used to classify geometries incorporating totally
geodesic submanifolds, such as those found in thick braneworld and other
5-dimensional scenarios.Comment: 9 pages, REVTeX4, in press in Phys. Rev.
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
Creation of fundamental particles in Wesson's IMT
Fundamental particles, regarded as the constituents of quarks and leptons,
are described classicaly in the framework of the Weyl-Dirac version of Wesson's
Induced Matter Theory. There are neutral particles and particles having charge
Q=+/-(1/3e). The particles appear on the 4D brane, our universe, and are filled
with a substance induced by the 5D bulk. This substace is taken to have mass
density, charge density, pressure and is characterized by the prematter eq. of
state P+\rho=0. The interior is separated from the surrounding vacuum by a
boundary surface where the 4D metric tensor satisfies an a'la Schwarzschild
condition. Outside of the boundary holds the Schwarzschild, or the
Reissner-Nordstroem Metric, while the particles are characterized by mass,
radius, charge.Comment: 29 pages. Submitted for publication in the Gen. Rel. and Grav.
Journa
Static wormholes on the brane inspired by Kaluza-Klein gravity
We use static solutions of 5-dimensional Kaluza-Klein gravity to generate
several classes of static, spherically symmetric spacetimes which are analytic
solutions to the equation , where is the
four-dimensional Ricci scalar. In the Randall & Sundrum scenario they can be
interpreted as vacuum solutions on the brane. The solutions contain the
Schwarzschild black hole, and generate new families of traversable Lorenzian
wormholes as well as nakedly singular spacetimes. They generalize a number of
previously known solutions in the literature, e.g., the temporal and spatial
Schwarzschild solutions of braneworld theory as well as the class of self-dual
Lorenzian wormholes. A major departure of our solutions from Lorenzian
wormholes {\it a la} Morris and Thorne is that, for certain values of the
parameters of the solutions, they contain three spherical surfaces (instead of
one) which are extremal and have finite area. Two of them have the same size,
meet the "flare-out" requirements, and show the typical violation of the energy
conditions that characterizes a wormhole throat. The other extremal sphere is
"flaring-in" in the sense that its sectional area is a local maximum and the
weak, null and dominant energy conditions are satisfied in its neighborhood.
After bouncing back at this second surface a traveler crosses into another
space which is the double of the one she/he started in. Another interesting
feature is that the size of the throat can be less than the Schwarzschild
radius , which no longer defines the horizon, i.e., to a distant observer
a particle or light falling down crosses the Schwarzschild radius in a finite
time
The bang of a white hole in the early universe from a 6D vacuum state: Origin of astrophysical spectrum
Using a previously introduced model in which the expansion of the universe is
driven by a single scalar field subject to gravitational attraction induced by
a white hole during the expansion (from a 6D vacuum state), we study the origin
of squared inflaton fluctuations spectrum on astrophysical scales.Comment: Final version to be published in Eur. Phys. J.
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
Non-perturbative scalar gauge-invariant metric fluctuations from the Ponce de Leon metric in the STM theory of gravity
We study our non-perturbative formalism to describe scalar gauge-invariant
metric fluctuations by extending the Ponce de Leon metric.Comment: accepted in Eur. Phys. J.
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
Static Observers in Curved Spaces and Non-inertial Frames in Minkowski Spacetime
Static observers in curved spacetimes may interpret their proper acceleration
as the opposite of a local gravitational field (in the Newtonian sense). Based
on this interpretation and motivated by the equivalence principle, we are led
to investigate congruences of timelike curves in Minkowski spacetime whose
acceleration field coincides with the acceleration field of static observers of
curved spaces. The congruences give rise to non-inertial frames that are
examined. Specifically we find, based on the locality principle, the embedding
of simultaneity hypersurfaces adapted to the non-inertial frame in an explicit
form for arbitrary acceleration fields. We also determine, from the Einstein
equations, a covariant field equation that regulates the behavior of the proper
acceleration of static observers in curved spacetimes. It corresponds to an
exact relativistic version of the Newtonian gravitational field equation. In
the specific case in which the level surfaces of the norm of the acceleration
field of the static observers are maximally symmetric two-dimensional spaces,
the energy-momentum tensor of the source is analyzed.Comment: 28 pages, 4 figures