263 research outputs found
Possible potentials responsible for stable circular relativistic orbits
Bertrand's theorem in classical mechanics of the central force fields
attracts us because of its predictive power. It categorically proves that there
can only be two types of forces which can produce stable, circular orbits. In
the present article an attempt has been made to generalize Bertrand's theorem
to the central force problem of relativistic systems. The stability criterion
for potentials which can produce stable, circular orbits in the relativistic
central force problem has been deduced and a general solution of it is
presented in the article. It is seen that the inverse square law passes the
relativistic test but the kind of force required for simple harmonic motion
does not. Special relativistic effects do not allow stable, circular orbits in
presence of a force which is proportional to the negative of the displacement
of the particle from the potential center.Comment: 11 pages, Latex fil
Gravitational lensing in spherically symmetric static spacetimes with centrifugal force reversal
In Schwarzschild spacetime the value of the radius coordinate is
characterized by three different properties: (a) there is a ``light sphere'',
(b) there is ``centrifugal force reversal'', (c) it is the upper limiting
radius for a non-transparent Schwarschild source to act as a gravitational lens
that produces infinitely many images. In this paper we prove a theorem to the
effect that these three properties are intimately related in {\em any}
spherically symmetric static spacetime. We illustrate the general results with
some examples including black-hole spacetimes and Morris-Thorne wormholes.Comment: 18 pages, 3 eps-figure
Wave propagation in axion electrodynamics
In this paper, the axion contribution to the electromagnetic wave propagation
is studied. First we show how the axion electrodynamics model can be embedded
into a premetric formalism of Maxwell electrodynamics. In this formalism, the
axion field is not an arbitrary added Chern-Simon term of the Lagrangian, but
emerges in a natural way as an irreducible part of a general constitutive
tensor.We show that in order to represent the axion contribution to the wave
propagation it is necessary to go beyond the geometric approximation, which is
usually used in the premetric formalism. We derive a covariant dispersion
relation for the axion modified electrodynamics. The wave propagation in this
model is studied for an axion field with timelike, spacelike and null
derivative covectors. The birefringence effect emerges in all these classes as
a signal of Lorentz violation. This effect is however completely different from
the ordinary birefringence appearing in classical optics and in premetric
electrodynamics. The axion field does not simple double the ordinary light cone
structure. In fact, it modifies the global topological structure of light cones
surfaces. In CFJ-electrodynamics, such a modification results in violation of
causality. In addition, the optical metrics in axion electrodynamics are not
pseudo-Riemannian. In fact, for all types of the axion field, they are even
non-Finslerian
On the energy functional on Finsler manifolds and applications to stationary spacetimes
In this paper we first study some global properties of the energy functional
on a non-reversible Finsler manifold. In particular we present a fully detailed
proof of the Palais--Smale condition under the completeness of the Finsler
metric. Moreover we define a Finsler metric of Randers type, which we call
Fermat metric, associated to a conformally standard stationary spacetime. We
shall study the influence of the Fermat metric on the causal properties of the
spacetime, mainly the global hyperbolicity. Moreover we study the relations
between the energy functional of the Fermat metric and the Fermat principle for
the light rays in the spacetime. This allows us to obtain existence and
multiplicity results for light rays, using the Finsler theory. Finally the case
of timelike geodesics with fixed energy is considered.Comment: 23 pages, AMSLaTeX. v4 matches the published versio
Gravitational dynamics for all tensorial spacetimes carrying predictive, interpretable and quantizable matter
Only a severely restricted class of tensor fields can provide classical
spacetime geometries, namely those that can carry matter field equations that
are predictive, interpretable and quantizable. These three conditions on matter
translate into three corresponding algebraic conditions on the underlying
tensorial geometry, namely to be hyperbolic, time-orientable and
energy-distinguishing. Lorentzian metrics, on which general relativity and the
standard model of particle physics are built, present just the simplest
tensorial spacetime geometry satisfying these conditions. The problem of
finding gravitational dynamics---for the general tensorial spacetime geometries
satisfying the above minimum requirements---is reformulated in this paper as a
system of linear partial differential equations, in the sense that their
solutions yield the actions governing the corresponding spacetime geometry.
Thus the search for modified gravitational dynamics is reduced to a clear
mathematical task.Comment: 47 pages, no figures, minor update
Local and global gravity
Our long experience with Newtonian potentials has inured us to the view that
gravity only produces local effects. In this paper we challenge this quite
deeply ingrained notion and explicitly identify some intrinsically global
gravitational effects. In particular we show that the global cosmological
Hubble flow can actually modify the motions of stars and gas within individual
galaxies, and even do so in a way which can apparently eliminate the need for
galactic dark matter. Also we show that a classical light wave acquires an
observable, global, path dependent phase in traversing a gravitational field.
Both of these effects serve to underscore the intrinsic difference between
non-relativistic and relativistic gravity.Comment: LaTeX, 20 pages plus three figures in two postscript files. To appear
in a special issue of Foundations of Physics honoring Professor Lawrence
Horwitz on the occasion of his 65th birthday; A. van der Merwe and S. Raby,
Editors, Plenum Publishing Company, N.Y., 199
Mathematics of Gravitational Lensing: Multiple Imaging and Magnification
The mathematical theory of gravitational lensing has revealed many generic
and global properties. Beginning with multiple imaging, we review
Morse-theoretic image counting formulas and lower bound results, and
complex-algebraic upper bounds in the case of single and multiple lens planes.
We discuss recent advances in the mathematics of stochastic lensing, discussing
a general formula for the global expected number of minimum lensed images as
well as asymptotic formulas for the probability densities of the microlensing
random time delay functions, random lensing maps, and random shear, and an
asymptotic expression for the global expected number of micro-minima. Multiple
imaging in optical geometry and a spacetime setting are treated. We review
global magnification relation results for model-dependent scenarios and cover
recent developments on universal local magnification relations for higher order
caustics.Comment: 25 pages, 4 figures. Invited review submitted for special issue of
General Relativity and Gravitatio
Gravitational lensing in the Kerr-Randers optical geometry
A new geometric method to determine the deflection of light in the equatorial
plane of the Kerr solution is presented, whose optical geometry is a surface
with a Finsler metric of Randers type. Applying the Gauss-Bonnet theorem to a
suitable osculating Riemannian manifold, adapted from a construction by Naz\i
m, it is shown explicitly how the two leading terms of the asymptotic
deflection angle of gravitational lensing can be found in this way.Comment: 7 pages, 1 figure. Accepted by Gen. Rel. Grav. Version 2: change of
notation in sec.
Weak-Lensing by Large-Scale Structure and the Polarization Properties of Distant Radio-Sources
We estimate the effects of weak lensing by large-scale density
inhomogeneities and long-wavelength gravitational waves upon the polarization
properties of electromagnetic radiation as it propagates from cosmologically
distant sources. Scalar (density) fluctuations do not rotate neither the plane
of polarization of the electromagnetic radiation nor the source image. They
produce, however, an appreciable shear, which distorts the image shape, leading
to an apparent rotation of the image orientation relative to its plane of
polarization. In sources with large ellipticity the apparent rotation is rather
small, of the order (in radians) of the dimensionless shear. The effect is
larger at smaller source eccentricity. A shear of 1% can induce apparent
rotations of around 5 degrees in radio sources with the smallest eccentricity
among those with a significant degree of integrated linear polarization. We
discuss the possibility that weak lensing by shear with rms value around or
below 5% may be the cause for the dispersion in the direction of integrated
linear polarization of cosmologically distant radio sources away from the
perpendicular to their major axis, as expected from models for their magnetic
fields. A rms shear larger than 5% would be incompatible with the observed
correlation between polarization properties and source orientation in distant
radio galaxies and quasars. Gravity waves do rotate both the plane of
polarization as well as the source image. Their weak lensing effects, however,
are negligible.Comment: 23 pages, 2 eps figures, Aastex 4.0 macros. Final version, as
accepted by ApJ. Additional references and some changes in the introduction
and conclusion
A generalized photon propagator
A covariant gauge independent derivation of the generalized dispersion
relation of electromagnetic waves in a medium with local and linear
constitutive law is presented. A generalized photon propagator is derived. For
Maxwell constitutive tensor, the standard light cone structure and the standard
Feynman propagator are reinstated
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