150 research outputs found
Calculation of permittivity tensors for invisibility devices by effective medium approach in general relativity
Permittivity tensors of arbitrary shaped invisibility devices are obtained
using effective medium approach in general relativity. As special cases,
analytical expressions for the permittivity tensors of invisibility cloaks for
the elliptic cylinder, prolate spheroid, and the confocal paraboloid geometry
are derived. In the case of elliptic cylinder, we found that the point of
infinite light speed in the electromagnetic space becomes two points in the
physical space in the zz component of the permittivity tensor. This result is
different from the case of perfect cylinder in which there is a line of cloak
at which the speed of light becomes infinite. In the cases of prolate spheroid
and confocal paraboloid, the point of infinite light speed in the
electromagnetic space becomes line in the physical space for the first two
tensor components and the third component of the permittivity tensor becomes
singular at the line of cloak
Gravitational energy of a magnetized Schwarzschild black hole - a teleparallel approach
We investigate the distribution of gravitational energy on the spacetime of a
Schwarzschild black hole immersed in a cosmic magnetic field. This is done in
the context of the {\it Teleparallel Equivalent of General Relativity}, which
is an alternative geometrical formulation of General Relativity, where gravity
is describe by a spacetime endowed with torsion, rather than curvature, with
the fundamental field variables being tetrads. We calculate the energy enclosed
by a two-surface of constant radius - in particular, the energy enclosed by the
event horizon of the black hole. In this case we find that the magnetic field
has the effect of increasing the gravitational energy as compared to the vacuum
Schwarzschild case. We also compute the energy (i) in the weak magnetic field
limit, (ii) in the limit of vanishing magnetic field, and (iii) in the absence
of the black hole. In all cases our results are consistent with what should be
expected on physical grounds.Comment: version to match the one to be published on General Relativity and
Gravitatio
Dark spinor models in gravitation and cosmology
We introduce and carefully define an entire class of field theories based on
non-standard spinors. Their dominant interaction is via the gravitational field
which makes them naturally dark; we refer to them as Dark Spinors. We provide a
critical analysis of previous proposals for dark spinors noting that they
violate Lorentz invariance. As a working assumption we restrict our analysis to
non-standard spinors which preserve Lorentz invariance, whilst being non-local
and explicitly construct such a theory. We construct the complete
energy-momentum tensor and derive its components explicitly by assuming a
specific projection operator. It is natural to next consider dark spinors in a
cosmological setting. We find various interesting solutions where the spinor
field leads to slow roll and fast roll de Sitter solutions. We also analyse
models where the spinor is coupled conformally to gravity, and consider the
perturbations and stability of the spinor.Comment: 43 pages. Several new sections and details added. JHEP in prin
The gauge theory of dislocations: static solutions of screw and edge dislocations
We investigate the T(3)-gauge theory of static dislocations in continuous
solids. We use the most general linear constitutive relations bilinear in the
elastic distortion tensor and dislocation density tensor for the force and
pseudomoment stresses of an isotropic solid. The constitutive relations contain
six material parameters. In this theory both the force and pseudomoment
stresses are asymmetric. The theory possesses four characteristic lengths l1,
l2, l3 and l4 which are given explicitely. We first derive the
three-dimensional Green tensor of the master equation for the force stresses in
the translational gauge theory of dislocations. We then investigate the
situation of generalized plane strain (anti-plane strain and plane strain).
Using the stress function method, we find modified stress functions for screw
and edge dislocations. The solution of the screw dislocation is given in terms
of one independent length l1=l4. For the problem of an edge dislocation, only
two characteristic lengths l2 and l3 arise with one of them being the same
l2=l1 as for the screw dislocation. Thus, this theory possesses only two
independent lengths for generalized plane strain. If the two lengths l2 and l3
of an edge dislocation are equal, we obtain an edge dislocation which is the
gauge theoretical version of a modified Volterra edge dislocation. In the case
of symmetric stresses we recover well known results obtained earlier.Comment: 33 pages, 17 figure
On Geometrically Unified Fields and Universal Constants
We consider the Cartan extension of Riemann geometry as the basis upon which
to build the Sciama--Kibble completion of Einstein gravity, developing the most
general theory in which torsion and metric have two independent coupling
constants: the main problem of the ESK theory was that torsion, having the
Newton constant, was negligible beyond the Planck scale, but in this
theory torsion, with its own coupling constant, may be
relevant much further Planck scales; further consequences of these
torsionally-induced interactions will eventually be discussed.Comment: 10 page
Dirac field in topologically massive gravity
We consider a Dirac field coupled minimally to the Mielke-Baekler model of
gravity and investigate cosmological solutions in three dimensions. We arrive
at a family of solutions which exists even in the limit of vanishing
cosmological constant.Comment: 12 pages. Title changed. Conclusion extended. Appendix added. To
appear in Gen. Rel. Gra
Generalized Chern-Simons Modified Gravity in First-Order Formalism
We propose a generalization of Chern-Simons (CS) modified gravity in
first-order formalism. CS modified gravity action has a term that comes from
the chiral anomaly which is Pontryagin invariant. First-order CS modified
gravity is a torsional theory and in a space-time with torsion the chiral
anomaly includes a torsional topological term called Nieh-Yan invariant. We
generalize the CS modified gravity by adding the Nieh-Yan term to the action
and find the effective theory. We compare the generalized theory with the
first-order CS modified gravity and comment on the similarities and
differences.Comment: 8 pages, an author added, new paragraphs, comments and references
added, published in Gen. Relativ. Gravi
Quantum systems in weak gravitational fields
Fully covariant wave equations predict the existence of a class of
inertial-gravitational effects that can be tested experimentally. In these
equations inertia and gravity appear as external classical fields, but, by
conforming to general relativity, provide very valuable information on how
Einstein's views carry through in the world of the quantum.Comment: 22 pages. To be published in Proceedings of the 17th Course of the
International School of Cosmology and Gravitation "Advances in the interplay
between quantum and gravity physics" edited by V. De Sabbata and A.
Zheltukhin, Kluwer Academic Publishers, Dordrech
Rotational elasticity and couplings to linear elasticity
It is the aim of the paper to present a new point of view on rotational
elasticity in a nonlinear setting using orthogonal matrices. The proposed
model, in the linear approximation, can be compared to the well known
equilibrium equations of static linear elasticity. An appropriate kinetic
energy is identified and we present a dynamical model of rotational elasticity.
The propagation of elastic waves in such a medium is studied and we find two
classes of waves, transversal rotational waves and longitudinal rotational
waves, both of which are solutions of the nonlinear partial differential
equations. For certain parameter choices, the transversal wave velocity can be
greater than the longitudinal wave velocity. Moreover, parameter ranges are
identified where the model describes an auxetic material. However, in all cases
the potential energy functional is positive definite. Finally, we couple the
rotational waves to linear elastic waves to study the behaviour of the coupled
system. We find wave like solutions to the coupled equations and can visualise
our results with the help of suitable figures.Comment: 19 pages, 2 figures, heavily revised and largely extended versio
Mach's Principle and the Origin of Inertia
The current status of Mach's principle is discussed within the context of
general relativity. The inertial properties of a particle are determined by its
mass and spin, since these characterize the irreducible unitary representations
of the inhomogeneous Lorentz group. The origin of the inertia of mass and
intrinsic spin are discussed and the inertia of intrinsic spin is studied via
the coupling of intrinsic spin with rotation. The implications of spin-rotation
coupling and the possibility of history dependence and nonlocality in
relativistic physics are briefly mentioned.Comment: 14 pages. Dedicated to Carl Brans in honor of his 80th birthday. To
appear in the Brans Festschrift; v2: typo corrected, published in: At the
Frontier of Spacetime, edited by T. Asselmeyer-Maluga (Springer, 2016),
Chapter 10, pp. 177-18
- …