208 research outputs found
FRW Universe Models in Conformally Flat Spacetime Coordinates. III: Universe models with positive spatial curvature
We deduce general expressions for the line element of universe models with
positive spatial curvature described by conformally flat spacetime coordinates.
Models with dust, radiation and vacuum energy are exhibited. Discussing the
existence of particle horizons we show that there is continual annihilation of
space, matter and energy in a dust and radiation dominated universe, and
continual creation in a LIVE domined universe when conformal time is used in
Friedmann-Robertson-Walker models with positive spatial curvature. A general
procedure is given for finding coordinates to be used in Penrose diagrams. We
also calculate the age and the redshift of some universe models using conformal
time.Comment: 22 pages, 9 figure
Relativistic contraction and related effects in noninertial frames
Although there is no relative motion among different points on a rotating
disc, each point belongs to a different noninertial frame. This fact, not
recognized in previous approaches to the Ehrenfest paradox and related
problems, is exploited to give a correct treatment of a rotating ring and a
rotating disc. Tensile stresses are recovered, but, contrary to the prediction
of the standard approach, it is found that an observer on the rim of the disc
will see equal lengths of other differently moving objects as an inertial
observer whose instantaneous position and velocity are equal to that of the
observer on the rim. The rate of clocks at various positions, as seen by
various observers, is also discussed. Some results are generalized for
observers arbitrarily moving in a flat or a curved spacetime. The generally
accepted formula for the space line element in a non-time-orthogonal frame is
found inappropriate in some cases. Use of Fermi coordinates leads to the result
that for any observer the velocity of light is isotropic and is equal to ,
providing that it is measured by propagating a light beam in a small
neighborhood of the observer.Comment: 15 pages, significantly revised version, title changed, to appear in
Phys. Rev.
FRW Universe Models in Conformally Flat Spacetime Coordinates. II: Universe models with negative and vanishing spatial curvature
We deduce general expressions for the line element of universe models with
negative and vanishing spatial curvature described by conformally flat
spacetime coordinates. The empty Milne universe model and models with dust,
radiation and vacuum energy are exhibited. Discussing the existence of particle
horizons we show that there is continual creation of space, matter and energy
when conformal time is used in Friedmann-Robertson-Walker models with negative
spatial curvature.Comment: 25 pages, 12 figure
On the twin paradox in static spacetimes: I. Schwarzschild metric
Motivated by a conjecture put forward by Abramowicz and Bajtlik we reconsider
the twin paradox in static spacetimes. According to a well known theorem in
Lorentzian geometry the longest timelike worldline between two given points is
the unique geodesic line without points conjugate to the initial point on the
segment joining the two points. We calculate the proper times for static twins,
for twins moving on a circular orbit (if it is a geodesic) around a centre of
symmetry and for twins travelling on outgoing and ingoing radial timelike
geodesics. We show that the twins on the radial geodesic worldlines are always
the oldest ones and we explicitly find the conjugate points (if they exist)
outside the relevant segments. As it is of its own mathematical interest, we
find general Jacobi vector fields on the geodesic lines under consideration. In
the first part of the work we investigate Schwarzschild geometry.Comment: 18 pages, paper accepted for publication in Gen. Rel. Gra
FRW Universe Models in Conformally Flat Spacetime Coordinates. I: General Formalism
The 3-space of a universe model is defined at a certain simultaneity. Hence
space depends on which time is used. We find a general formula generating all
known and also some new transformations to conformally flat spacetime
coordinates. A general formula for the recession velocity is deduced.Comment: 12 page
Magnetohydrodynamics in the Inflationary Universe
Magnetohydrodynamic (MHD) waves are analysed in the early Universe, in the
inflationary era, assuming the Universe to be filled with a nonviscous fluid of
the Zel'dovich type () in a metric of the de Sitter form. A spatially
uniform, time dependent, magnetic field is assumed to be present.
The Einstein equations are first solved to give the time dependence of the
scale factor, assuming that the matter density, but not the magnetic field,
contribute as source terms. The various modes are thereafter analysed; they
turn out to be essentially of the same kind as those encountered in
conventional nongravitational MHD, although the longitudinal magnetosonic wave
is not interpretable as a physical energy-transporting wave as the group
velocity becomes superluminal. We determine the phase speed of the various
modes; they turn out to be scale factor independent. The Alfv\'{e}n velocity of
the transverse magnetohydrodynamic wave becomes extremely small in the
inflationary era, showing that the wave is in practice 'frozen in'.Comment: 19 pages, LaTeX, no figures. Minor additions to the Summary section
and Acknowledgments section. Two new references. Version to appear in Phys.
Rev.
Randall-Sundrum Model in the Presence of a Brane Bulk Viscosity
The presence of a bulk viscosity for the cosmic fluid on a single
Randall-Sundrum brane is considered. The spatial curvature is assumed to be
zero. The five-dimensional Friedmann equation is derived, together with the
energy conservation equation for the viscous fluid. These governing equations
are solved for some special cases: (i) in the low-energy limit when the matter
energy density is small compared with brane tension; (ii) for a
matter-dominated universe, and (iii) for a radiation-dominated universe. Rough
numerical estimates, for the extreme case when the universe is at its Planck
time, indicate that the viscous effect can be significant.Comment: 18 pages, RevTeX4, no figures. Discussion in Sec. III expanded; new
references. To appear in Phys. Rev.
The Relative Space: Space Measurements on a Rotating Platform
We introduce here the concept of relative space, an extended 3-space which is
recognized as the only space having an operational meaning in the study of the
space geometry of a rotating disk. Accordingly, we illustrate how space
measurements are performed in the relative space, and we show that an old-aged
puzzling problem, that is the Ehrenfest's paradox, is explained in this purely
relativistic context. Furthermore, we illustrate the kinematical origin of the
tangential dilation which is responsible for the solution of the Ehrenfest's
paradox.Comment: 14 pages, 2 EPS figures, LaTeX, to appear in the European Journal of
Physic
Evolution of the Bianchi I, the Bianchi III and the Kantowski-Sachs Universe: Isotropization and Inflation
We study the Einstein-Klein-Gordon equations for a convex positive potential
in a Bianchi I, a Bianchi III and a Kantowski-Sachs universe. After analysing
the inherent properties of the system of differential equations, the study of
the asymptotic behaviors of the solutions and their stability is done for an
exponential potential. The results are compared with those of Burd and Barrow.
In contrast with their results, we show that for the BI case isotropy can be
reached without inflation and we find new critical points which lead to new
exact solutions. On the other hand we recover the result of Burd and Barrow
that if inflation occurs then isotropy is always reached. The numerical
integration is also done and all the asymptotical behaviors are confirmed.Comment: 22 pages, 12 figures, Self-consistent Latex2e File. To be published
in Phys. Rev.
Magnetic Surfaces in Stationary Axisymmetric General Relativity
In this paper a new method is derived for constructing electromagnetic
surface sources for stationary axisymmetric electrovac spacetimes endowed with
non-smooth or even discontinuous
Ernst potentials. This can be viewed as a generalization of some classical
potential theory results, since lack of continuity of the potential is related
to dipole density and lack of smoothness, to monopole density. In particular
this approach is useful for constructing the dipole source for the magnetic
field. This formalism involves solving a linear elliptic differential equation
with boundary conditions at infinity. As an example, two different models of
surface densities for the Kerr-Newman electrovac spacetime are derived.Comment: 15 page
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