139 research outputs found
Congruence Kinematics in Conformal Gravity
In this paper we calculate the kinematical quantities of the Raychaudhuri
equations, to characterize a congruence of time-like integral curves, according
to the vacuum radial solution of Weyl theory of gravity. Also the corresponding
flows are plotted for definite values of constants.Comment: 10 pages, 3 figure
Homothetic Congruences in General Relativity
The kinematical characteristics of distinct infalling homothetic fields are
discussed by specifying the transverse subspace of their generated congruences
to the energy-momentum deposit of the chosen gravitational system. This is
pursued through the inclusion of the base manifold's cotangent bundle in a
generalized Raychaudhuri equation and its kinematical expressions. Exploiting
an electromagnetic energy-momentum tensor as the source of non-gravitational
effects, I investigate the evolution of the mentioned homothetic congruences,
as they fall onto a Reissner-Nordstrom black hole. The results show remarkable
differences to the common expectations from infalling congruences of massive
particles.Comment: 19 pages, 15 figure
Congruence Convergence in pp-wave Spacetime
We argue that the well-known geodesic completeness property of pp-waves, can
be disregarded once the geodesics are extracted as being extended along sets of
Brinkmann coordinates. This issue is investigated in the more general context
of congruence convergence and we show that the problem leads to diverse issues
for non-geodesic congruences. The discussion is mostly based on the null
congruence expansion and a generalized Raychaudhuri equation is also provided.Comment: 14 pages, 2 figure
Surface configuration in gravity
We investigate the conditions on the additional constant in the
so-called theory of gravity, due to existence of different kinds of
space-like surfaces in both weak field and strong field limits, and their
possible correspondence to black hole event horizons. Adopting a Schwarzschild
limit, we probe the behaviour of in different contexts of radial and
radial-rotational congruence of null geodesics. We show that these cases serve
as correspondents to black hole horizons in some peculiar cases of study.Comment: 10 pages, 9 figure
Massive Gravitons on Bohmian Congruences
Taking a quantum corrected form of Raychaudhuri equation in a geometric
background described by a Lorentz-violating massive theory of gravity, we go
through investigating a time-like congruence of massive gravitons affected by a
Bohmian quantum potential. We find some definite conditions upon which these
gravitons are confined to diverging Bohmian trajectories. The respective
behaviour of those quantum potentials are also derived and discussed.
Additionally, and through a relativistic quantum treatment of a typical wave
function, we demonstrate schematic conditions on the associated frequency to
the gravitons, in order to satisfy the necessity of divergence.Comment: 9 pages, 9 figure
Focusing of world-lines in Weyl gravity
We study the evolution of time-like congruences in the vacuum solutions of
Weyl conformal theory of gravity. Using the Raycaudhuri equation, we show that
for positive values of the coeffcient of the linear term in the solution and in
the absence of the cosmological constant, the incoming rays converge. The
evolution of the congruence for negative values is investigated for different
values of the parameters. The behavior of the congruence under conformal
transformations is also studied.Comment: 3 eps figure
Numerical modeling of rocking of shallow foundations subjected to slow cyclic loading with consideration of soil-structure interaction
Strong Vibration of buildings during seismic or wind loading may result in an
uplift or partial separation of the foundation from the underneath soil. To
date, various researches have indicated that Soil-Structure Interaction (SSI)
has many favorable features including a probable increase in natural period of
the soil-structure system and also a decrease in shear base demand in
structures. Furthermore, Rocking is one of the most important factors in
describing the rotational behavior of a structure built on a shallow foundation
especially on a soft soil which can affect the dynamic behavior of the
structure noticeably. To study the effects of rocking of shallow foundations
subjected to slow cyclic loading with consideration of soil-structure
interaction, a Finite Element Method (FEM) using ABAQUS software has been
deployed to simulate the rocking motion of shallow foundations. For a more
efficient simulation of the soil, both linear and non-linear elasto-plastic
behavior of the soil has been taken into account in the analysis using the
sub-routine coded in FORTRAN. The results notably show that allowing the
foundation to rock may result in stiffness degradation of the soil-structure
system and an increase in energy dissipation of soil-structure, especially in
high rise structures. Additionally, results describe that deploying the linear
elastic-perfect plastic approach may result in higher uplift of the foundation
in comparison to that using a non-linear elasto-plastic approach, particularly
in structures with lower heights
Cartographic distortions make dielectric spacetime analog models imperfect mimickers
It is commonly assumed that if the optical metric of a dielectric medium is
identical to the metric of a vacuum space-time then light propagation through
the dielectric mimics light propagation in the vacuum. However, just as the
curved surface of the Earth cannot be mapped into a flat plane without
distortion of some surface features, so too is it impossible to project the
behavior of light from the vacuum into a dielectric analog residing in
Minkowski space-time without introducing distortions. We study the covariance
properties of dielectric analog space-times and the kinematics of a congruence
of light in the analog, and show how certain features can be faithfully
emulated in the analog depending on the choice of projection, but that not all
features can be simultaneously emulated without distortion. These findings
indicate conceptual weaknesses in the idea of using analog space-times as a
basis for transformation optics, and we show that a certain formulation of
transformation optics closely related to analog space-times resolves these
issues.Comment: 15 pages, 4 figure
Covariant kinematics of light in media and a generalized Raychaudhuri equation
There is ongoing interest in adopting various tools and ideas from general
relativity for optical applications and the study of light propagation through
natural or engineered media. Here, the covariant kinematics of light
propagating through arbitrary dielectric media in curved space-times are
derived, allowing for analysis and tracing of congruences of light through
media that may smoothly vary in character between vacuum, positively
refracting, and negatively refracting; or null, timelike, and spacelike with
respect to the background metric. The kinematics are then used to generalize
the Raychaudhuri equation -- an important tool in general relativity that
describes the focus of a congruence. These results will be useful for the
analysis of optical devices, particularly those designed using transformation
optics, and serve as theoretical tools to study generalized concepts in general
relativity.Comment: 22 pages, 1 figure. This version has changes to conform with version
published in Phys Rev
Shrinking cloaks in expanding spacetimes: the role of coordinates and the meaning of transformations in Transformation Optics
The fully covariant formulation of transformation optics is used to find the
configuration of a cloaking device operating in an expanding universe modelled
by a Friedmann-Lema\^itre-Robertson-Walker spacetime. This spacetime cloak is
used as a platform for probing the covariant formulation of transformation
optics, thereby rigorously enhancing the conceptual understanding of the
theory. By studying the problem in both comoving and physical coordinates we
explicitly demonstrate the preservation of general covariance of
electrodynamics under the transformation optics procedure. This platform also
enables a detailed study of the various transformations that arise in
transformation optics. We define a corporeal transformation as the
"transformation" of transformation optics, and distinguish it from coordinate
and frame transformations. We find that corporeal transformations considered in
the literature have generally been restricted to a subset of all possible
corporeal transformations, providing a potential mechanism for increased
functionality of transformation optics.Comment: 24 pages, 4 figure
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