1,227 research outputs found
Exact General Relativistic Thick Disks
A method to construct exact general relativistic thick disks that is a simple
generalization of the ``displace, cut and reflect'' method commonly used in
Newtonian, as well as, in Einstein theory of gravitation is presented. This
generalization consists in the addition of a new step in the above mentioned
method. The new method can be pictured as a ``displace, cut, {\it fill} and
reflect'' method. In the Newtonian case, the method is illustrated in some
detail with the Kuzmin-Toomre disk. We obtain a thick disk with acceptable
physical properties. In the relativistic case two solutions of the Weyl
equations, the Weyl gamma metric (also known as Zipoy-Voorhees metric) and the
Chazy-Curzon metric are used to construct thick disks. Also the Schwarzschild
metric in isotropic coordinates is employed to construct another family of
thick disks. In all the considered cases we have non trivial ranges of the
involved parameter that yield thick disks in which all the energy conditions
are satisfied.Comment: 11 pages, RevTex, 9 eps figs. Accepted for publication in PR
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
Induced inflation from a 5D purely kinetic scalar field formalism on warped product spaces
Considering a separable and purely kinetic 5D scalar field on a warped
product metric background we propose a new and more general approach for
inducing 4D scalar potentials on a 4D constant foliation of the 5D space-time.
We obtain an induced potential for a true 4D scalar field instead of a
potential for an effective 4D scalar field. In this formalism we can recover
the usual 4D inflationary formalism with a geometrically induced inflationary
potential. In addition the quantum confinement of the inflaton modes is
obtained naturally from the model for at least a class of warping factors.
Besides the 4D inflationary physics that results of this formalism is
independent of the 4D-hypersurface chosen.Comment: 8 pages Accepted for publication in European Physical Journal
Inducing the cosmological constant from five-dimensional Weyl space
We investigate the possibility of inducing the cosmological constant from
extra dimensions by embedding our four-dimensional Riemannian space-time into a
five-dimensional Weyl integrable space. Following approach of the induced
matter theory we show that when we go down from five to four dimensions, the
Weyl field may contribute both to the induced energy-tensor as well as to the
cosmological constant, or more generally, it may generate a time-dependent
cosmological parameter. As an application, we construct a simple cosmological
model which has some interesting properties.Comment: 7 page
Modified Brans-Dicke theory of gravity from five-dimensional vacuum
We investigate, in the context of five-dimensional (5D) Brans-Dicke theory of
gravity, the idea that macroscopic matter configurations can be generated from
pure vacuum in five dimensions, an approach first proposed in the framework of
general relativity. We show that the 5D Brans-Dicke vacuum equations when
reduced to four dimensions lead to a modified version of Brans-Dicke theory in
four dimensions (4D). As an application of the formalism, we obtain two
five-dimensional extensions of four-dimensional O'Hanlon and Tupper vacuum
solution and show that they lead two different cosmological scenarios in 4D.Comment: 9 page
Relativistic Static Thin Disks: The Counter-Rotating Model
A detailed study of the Counter-Rotating Model (CRM) for generic finite
static axially symmetric thin disks with nonzero radial pressure is presented.
We find a general constraint over the counter-rotating tangential velocities
needed to cast the surface energy-momentum tensor of the disk as the
superposition of two counter-rotating perfect fluids. We also found expressions
for the energy density and pressure of the counter-rotating fluids. Then we
shown that, in general, there is not possible to take the two counter-rotating
fluids as circulating along geodesics neither take the two counter-rotating
tangential velocities as equal and opposite. An specific example is studied
where we obtain some CRM with well defined counter-rotating tangential
velocities and stable against radial perturbations. The CRM obtained are in
agree with the strong energy condition, but there are regions of the disks with
negative energy density, in violation of the weak energy condition.Comment: 19 pages, 6 figures. Submitted to Physical Review
Electrovacuum Static Counterrotating Relativistic Dust Disks
A detailed study is presented of the counterrotating model (CRM) for generic
electrovacuum static axially symmetric relativistic thin disks without radial
pressure. We find a general constraint over the counterrotating tangential
velocities needed to cast the surface energy-momentum tensor of the disk as the
superposition of two counterrotating charged dust fluids. We also find explicit
expressions for the energy densities, charge densities and velocities of the
counterrotating fluids. We then show that this constraint can be satisfied if
we take the two counterrotating streams as circulating along electro-geodesics.
However, we show that, in general, it is not possible to take the two
counterrotating fluids as circulating along electro-geodesics nor take the two
counterrotating tangential velocities as equal and opposite. Four simple
families of models of counterrotating charged disks based on Chazy-Curzon-like,
Zipoy-Voorhees-like, Bonnor-Sackfield-like and Kerr-like electrovacuum
solutions are considered where we obtain some disks with a CRM well behaved.
The models are constructed using the well-known ``displace, cut and reflect''
method extended to solutions of vacuum Einstein-Maxwell equations.Comment: 19 pages, 16 figures, revtex
FRW Cosmology From Five Dimensional Vacuum Brans-Dicke Theory
We follow approach of induced matter theory for 5D vacuum BD, introduce
induced matter and potential in 4D hypersurfaces, and employ generalized FRW
type solution. We confine ourselves to scalar field and scale factors be
functions of the time. This makes the induced potential, by its definition,
vanishes. When the scale factor of fifth dimension and scalar field are not
constants, 5D eqs for any geometry admit a power law relation between scalar
field and scale factor of fifth dimension. Hence the procedure exhibits that 5D
vacuum FRW like eqs are equivalent, in general, to corresponding 4D vacuum ones
with the same spatial scale factor but new scalar field and coupling constant.
We show that 5D vacuum FRW like eqs or its equivalent 4D vacuum ones admit
accelerated solutions. For constant scalar field, eqs reduce to usual FRW eqs
with typical radiation dominated universe. For this situation we obtain
dynamics of scale factors for any geometry without any priori assumption. For
nonconstant scalar fields and spatially flat geometries, solutions are found to
be power law and exponential ones. We also employ weak energy condition for
induced matter, that allows negative/positive pressures. All types of solutions
fulfill WEC in different ranges. The power law solutions with negative/positive
pressures admit both decelerating and accelerating ones. Some solutions accept
shrinking extra dimension. By considering nonghost scalar fields and recent
observational measurements, solutions are more restricted. We illustrate that
accelerating power law solutions, which satisfy WEC and have nonghost fields,
are compatible with recent observations in ranges -4/3 < \omega </- -1.3151 and
1.5208 </- n < 1.9583 for dependence of fifth dimension scale factor with usual
scale factor. These ranges also fulfill condition nonghost fields in the
equivalent 4D vacuum BD eqs.Comment: 18 pages, 16 figures, 11 table
Exact General Relativistic Perfect Fluid Disks with Halos
Using the well-known ``displace, cut and reflect'' method used to generate
disks from given solutions of Einstein field equations, we construct static
disks made of perfect fluid based on vacuum Schwarzschild's solution in
isotropic coordinates. The same method is applied to different exactsolutions
to the Einstein'sequations that represent static spheres of perfect fluids. We
construct several models of disks with axially symmetric perfect fluid halos.
All disks have some common features: surface energy density and pressures
decrease monotonically and rapidly with radius. As the ``cut'' parameter
decreases, the disks become more relativistic, with surface energy density and
pressure more concentrated near the center. Also regions of unstable circular
orbits are more likely to appear for high relativistic disks. Parameters can be
chosen so that the sound velocity in the fluid and the tangential velocity of
test particles in circular motion are less then the velocity of light. This
tangential velocity first increases with radius and reaches a maximum.Comment: 22 pages, 25 eps.figs, RevTex. Phys. Rev. D to appea
Higher dimensional radiation collapse and cosmic censorship
We study the occurrence of naked singularities in the spherically symmetric
collapse of radiation shells in a higher dimensional spacetime. The necessary
conditions for the formation of a naked singularity or a black hole are
obtained. The naked singularities are found to be strong in the Tipler's sense
and thus violating cosmic censorship conjecture.Comment: 4 pages, ReVTeX, Phys Rev D Vol 62 107502 (2000
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