108 research outputs found
Direction of light propagation to order G^2 in static, spherically symmetric spacetimes: a new derivation
A procedure avoiding any integration of the null geodesic equations is used
to derive the direction of light propagation in a three-parameter family of
static, spherically symmetric spacetimes within the post-post-Minkowskian
approximation. Quasi-Cartesian isotropic coordinates adapted to the symmetries
of spacetime are systematically used. It is found that the expression of the
angle formed by two light rays as measured by a static observer staying at a
given point is remarkably simple in these coordinates. The attention is mainly
focused on the null geodesic paths that we call the "quasi-Minkowskian light
rays". The vector-like functions characterizing the direction of propagation of
such light rays at their points of emission and reception are firstly obtained
in the generic case where these points are both located at a finite distance
from the centre of symmetry. The direction of propagation of the
quasi-Minkowskian light rays emitted at infinity is then straightforwardly
deduced. An intrinsic definition of the gravitational deflection angle relative
to a static observer located at a finite distance is proposed for these rays.
The expression inferred from this definition extends the formula currently used
in VLBI astrometry up to the second order in the gravitational constant G.Comment: 19 pages; revised introduction; added references for introduction;
corrected typos; published in Class. Quantum Gra
Covariant Calculation of General Relativistic Effects in an Orbiting Gyroscope Experiment
We carry out a covariant calculation of the measurable relativistic effects
in an orbiting gyroscope experiment. The experiment, currently known as Gravity
Probe B, compares the spin directions of an array of spinning gyroscopes with
the optical axis of a telescope, all housed in a spacecraft that rolls about
the optical axis. The spacecraft is steered so that the telescope always points
toward a known guide star. We calculate the variation in the spin directions
relative to readout loops rigidly fixed in the spacecraft, and express the
variations in terms of quantities that can be measured, to sufficient accuracy,
using an Earth-centered coordinate system. The measurable effects include the
aberration of starlight, the geodetic precession caused by space curvature, the
frame-dragging effect caused by the rotation of the Earth and the deflection of
light by the Sun.Comment: 7 pages, 1 figure, to be submitted to Phys. Rev.
A generalized lens equation for light deflection in weak gravitational fields
A generalized lens equation for weak gravitational fields in Schwarzschild
metric and valid for finite distances of source and observer from the light
deflecting body is suggested. The magnitude of neglected terms in the
generalized lens equation is estimated to be smaller than or equal to 15 Pi/4
(m/d')^2, where m is the Schwarzschild radius of massive body and d' is
Chandrasekhar's impact parameter. The main applications of this generalized
lens equation are extreme astrometrical configurations, where 'Standard
post-Newtonian approach' as well as 'Classical lens equation' cannot be
applied. It is shown that in the appropriate limits the proposed lens equation
yields the known post-Newtonian terms, 'enhanced' post-post-Newtonian terms and
the Classical lens equation, thus provides a link between these both essential
approaches for determining the light deflection.Comment: 11 pages, 3 figure
Relativistic positioning: four-dimensional numerical approach in Minkowski space-time
We simulate the satellite constellations of two Global Navigation Satellite
Systems: Galileo (EU) and GPS (USA). Satellite motions are described in the
Schwarzschild space-time produced by an idealized spherically symmetric non
rotating Earth. The trajectories are then circumferences centered at the same
point as Earth. Photon motions are described in Minkowski space-time, where
there is a well known relation, Coll, Ferrando & Morales-Lladosa (2010),
between the emission and inertial coordinates of any event. Here, this relation
is implemented in a numerical code, which is tested and applied. The first
application is a detailed numerical four-dimensional analysis of the so-called
emission coordinate region and co-region. In a second application, a GPS
(Galileo) satellite is considered as the receiver and its emission coordinates
are given by four Galileo (GPS) satellites. The bifurcation problem (double
localization) in the positioning of the receiver satellite is then pointed out
and discussed in detail.Comment: 16 pages, 9 figures, published (online) in Astrophys. Space Sc
Nonminimal isotropic cosmological model with Yang-Mills and Higgs fields
We establish a nonminimal Einstein-Yang-Mills-Higgs model, which contains six
coupling parameters. First three parameters relate to the nonminimal coupling
of non-Abelian gauge field and gravity field, two parameters describe the
so-called derivative nonminimal coupling of scalar multiplet with gravity
field, and the sixth parameter introduces the standard coupling of scalar field
with Ricci scalar. The formulated six-parameter nonminimal
Einstein-Yang-Mills-Higgs model is applied to cosmology. We show that there
exists a unique exact cosmological solution of the de Sitter type for a special
choice of the coupling parameters. The nonminimally extended Yang-Mills and
Higgs equations are satisfied for arbitrary gauge and scalar fields, when the
coupling parameters are specifically related to the curvature constant of the
isotropic spacetime. Basing on this special exact solution we discuss the
problem of a hidden anisotropy of the Yang-Mills field, and give an explicit
example, when the nonminimal coupling effectively screens the anisotropy
induced by the Yang-Mills field and thus restores the isotropy of the model.Comment: 15 pages, revised version accepted to Int. J. Mod. Phys. D, typos
correcte
On Higher Order Gravities, Their Analogy to GR, and Dimensional Dependent Version of Duff's Trace Anomaly Relation
An almost brief, though lengthy, review introduction about the long history
of higher order gravities and their applications, as employed in the
literature, is provided. We review the analogous procedure between higher order
gravities and GR, as described in our previous works, in order to highlight its
important achievements. Amongst which are presentation of an easy
classification of higher order Lagrangians and its employment as a
\emph{criteria} in order to distinguish correct metric theories of gravity. For
example, it does not permit the inclusion of only one of the second order
Lagrangians in \emph{isolation}. But, it does allow the inclusion of the
cosmological term. We also discuss on the compatibility of our procedure and
the Mach idea. We derive a dimensional dependent version of Duff's trace
anomaly relation, which in \emph{four}-dimension is the same as the usual Duff
relation. The Lanczos Lagrangian satisfies this new constraint in \emph{any}
dimension. The square of the Weyl tensor identically satisfies it independent
of dimension, however, this Lagrangian satisfies the previous relation only in
three and four dimensions.Comment: 30 pages, added reference
Singularities in scalar-tensor gravity
The analysis of certain singularities in scalar-tensor gravity contained in a
recent paper is completed, and situations are pointed out in which these
singularities cannot occur.Comment: 6 pages, LaTe
Cosmological dynamics of R^n gravity
A detailed analysis of dynamics of cosmological models based on
gravity is presented. We show that the cosmological equations can be written as
a first order autonomous system and analyzed using the standard techniques of
dynamical system theory. In absence of perfect fluid matter, we find exact
solutions whose behavior and stability are analyzed in terms of the values of
the parameter . When matter is introduced, the nature of the (non-minimal)
coupling between matter and higher order gravity induces restrictions on the
allowed values of . Selecting such intervals of values and following the
same procedure used in the vacuum case, we present exact solutions and analyze
their stability for a generic value of the parameter . From this analysis
emerges the result that for a large set of initial conditions an accelerated
expansion is an attractor for the evolution of the cosmology. When matter
is present a transient almost-Friedman phase can also be present before the
transition to an accelerated expansion.Comment: revised and extended version, 35 pages, 12 tables, 14 figures which
are not included and can be found at http://www.mth.uct.ac.za/~peter/R
Dark Matter Gravitational Interactions
We argue that the conjectured dark mater in the Universe may be endowed with
a new kind of gravitational charge that couples to a short range gravitational
interaction mediated by a massive vector field. A model is constructed that
assimilates this concept into ideas of current inflationary cosmology. The
model is also consistent with the observed behaviour of galactic rotation
curves according to Newtonian dynamics. The essential idea is that stars
composed of ordinary (as opposed to dark matter) experience Newtonian forces
due to the presence of an all pervading background of massive gravitationally
charged cold dark matter. The novel gravitational interactions are predicted to
have a significant influence on pre-inflationary cosmology. The precise details
depend on the nature of a gravitational Proca interaction and the description
of matter. A gravitational Proca field configuration that gives rise to
attractive forces between dark matter charges of like polarity exhibits
homogeneous isotropic eternal cosmologies that are free of cosmological
curvature singularities thus eliminating the horizon problem associated with
the standard big-bang scenario. Such solutions do however admit dense hot
pre-inflationary epochs each with a characteristic scale factor that may be
correlated with the dark matter density in the current era of expansion. The
model is based on a theory in which a modification of Einsteinian gravity at
very short distances can be expressed in terms of the gradient of the Einstein
metric and the torsion of a non-Riemannian connection on the bundle of linear
frames over spacetime. Indeed we demonstrate that the genesis of the model
resides in a remarkable simplification that occurs when one analyses the
variational equations associated with a broad class of non-Riemannian actions.Comment: 40 pages, 4 Postscript figure
Dynamics of f(R)-cosmologies containing Einstein static models
We study the dynamics of homogeneous isotropic FRW cosmologies with positive
spatial curvature in -gravity, paying special attention to the existence
of Einstein static models and only study forms of for which these
static models have been shown to exist. We construct a compact state space and
identify past and future attractors of the system and recover a previously
discovered future attractor corresponding to an expanding accelerating model.
We also discuss the existence of universes which have both a past and future
bounce, a phenomenon which is absent in General Relativity.Comment: 14 pages, 6 figure
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