1,477 research outputs found
Teleparallel Theories of Gravity: Illuminating a Fully Invariant Approach
Teleparallel gravity and its popular generalization gravity can be
formulated as fully invariant (under both coordinate transformations and local
Lorentz transformations) theories of gravity. Several misconceptions about
teleparallel gravity and its generalizations can be found in the literature,
especially regarding their local Lorentz invariance. We describe how these
misunderstandings may have arisen and attempt to clarify the situation. In
particular, the central point of confusion in the literature appears to be
related to the inertial spin connection in teleparallel gravity models. While
inertial spin connections are commonplace in special relativity, and not
something inherent to teleparallel gravity, the role of the inertial spin
connection in removing the spurious inertial effects within a given frame of
reference is emphasized here. The careful consideration of the inertial spin
connection leads to the construction of a fully invariant theory of
teleparallel gravity and its generalizations. Indeed, it is the nature of the
spin connection that differentiates the relationship between what have been
called good tetrads and bad tetrads and clearly shows that, in principle, any
tetrad can be utilized. The field equations for the fully invariant formulation
of teleparallel gravity and its generalizations are presented and a number of
examples using different assumptions on the frame and spin connection are
displayed to illustrate the covariant procedure. Various modified teleparallel
gravity models are also briefly reviewed.Comment: v2: 72 pages, revised version, references added, matches published
versio
Models of light-like charges with non-geodesic world lines
Massless particles in General Relativity move with the speed of light, their
trajectories in spacetime are described by null geodesics. This is independent
of the electrical charge of the particle being considered, however, the charged
light-like case is less well understood. Starting with the Maxwell field of a
charged particle having a light-like geodesic world line in Minkowskian
space-time we construct the Maxwell field of such a particle having a
non-geodesic, light-like world line. The necessary geometry in the
neighbourhood of an arbitrary null world line in Minkowskian space-time is
described and properties of the resulting electromagnetic field are discussed.
The electromagnetic field obtained represents a light-like analogue of the
Lienard-Wiechert field, which generalises the Coulomb field of a charge having
a time-like geodesic world line to the field of a charge having an accelerated
world line.Comment: 11 pages, 1 figur
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
Conformal Invariance in Einstein-Cartan-Weyl space
We consider conformally invariant form of the actions in Einstein, Weyl,
Einstein-Cartan and Einstein-Cartan-Weyl space in general dimensions() and
investigate the relations among them. In Weyl space, the observational
consistency condition for the vector field determining non-metricity of the
connection can be obtained from the equation of motion. In Einstein-Cartan
space a similar role is played by the vector part of the torsion tensor. We
consider the case where the trace part of the torsion is the Kalb-Ramond type
of field. In this case, we express conformally invariant action in terms of two
scalar fields of conformal weight -1, which can be cast into some interesting
form. We discuss some applications of the result.Comment: 10 pages, version to appear MPL
Angular size test on the expansion of the Universe
Assuming the standard cosmological model as correct, the average linear size
of galaxies with the same luminosity is six times smaller at z=3.2 than at z=0,
and their average angular size for a given luminosity is approximately
proportional to 1/z. Neither the hypothesis that galaxies which formed earlier
have much higher densities nor their luminosity evolution, mergers ratio, or
massive outflows due to a quasar feedback mechanism are enough to justify such
a strong size evolution. Also, at high redshift, the intrinsic ultraviolet
surface brightness would be prohibitively high with this evolution, and the
velocity dispersion much higher than observed. We explore here another
possibility to overcome this problem by considering different cosmological
scenarios that might make the observed angular sizes compatible with a weaker
evolution.
One of the models explored, a very simple phenomenological extrapolation of
the linear Hubble law in a Euclidean static universe, fits the angular size vs.
redshift dependence quite well, which is also approximately proportional to 1/z
with this cosmological model. There are no free parameters derived ad hoc,
although the error bars allow a slight size/luminosity evolution. The type Ia
supernovae Hubble diagram can also be explained in terms of this model with no
ad hoc fitted parameter.
WARNING: I do not argue here that the true Universe is static. My intention
is just to discuss which theoretical models provide a better fit to the data of
observational cosmology.Comment: 44 pages, accepted to be published in Int. J. Mod. Phys.
Covariant gravitational dynamics in 3+1+1 dimensions
We develop a 3+1+1 covariant formalism with cosmological and astrophysical
applications. First we give the evolution and constraint equations both on the
brane and off-brane in terms of 3-space covariant kinematical,
gravito-electro-magnetic (Weyl) and matter variables. We discuss the junction
conditions across the brane in terms of the new variables. Then we establish a
closure condition for the equations on the brane. We also establish the
connection of this formalism with isotropic and anisotropic cosmological
brane-worlds. Finally we derive a new brane solution in the framework of our
formalism: the tidal charged Taub-NUT-(A)dS brane, which obeys the closure
condition.Comment: 35 pages 1 fig; significantly expanded with (a) new closure condition
on the brane, (b) discussion of anisotropic brane-worlds, (c) stationary
vacuum space-times with local rotational symmetry including (d) a new tidal
charged Taub-NUT-(A)dS brane solution; published version
Classical big-bounce cosmology: dynamical analysis of a homogeneous and irrotational Weyssenhoff fluid
A dynamical analysis of an effective homogeneous and irrotational Weyssenhoff
fluid in general relativity is performed using the 1+3 covariant approach that
enables the dynamics of the fluid to be determined without assuming any
particular form for the space-time metric. The spin contributions to the field
equations produce a bounce that averts an initial singularity, provided that
the spin density exceeds the rate of shear. At later times, when the spin
contribution can be neglected, a Weyssenhoff fluid reduces to a standard
cosmological fluid in general relativity. Numerical solutions for the time
evolution of the generalised scale factor in spatially-curved models are
presented, some of which exhibit eternal oscillatory behaviour without any
singularities. In spatially-flat models, analytical solutions for particular
values of the equation-of-state parameter are derived. Although the scale
factor of a Weyssenhoff fluid generically has a positive temporal curvature
near a bounce, it requires unreasonable fine tuning of the equation-of-state
parameter to produce a sufficiently extended period of inflation to fit the
current observational data.Comment: 34 pages, 18 figure
Inflating wormholes in the braneworld models
The braneworld model, in which our Universe is a three-brane embedded in a
five-dimensional bulk, allows the existence of wormholes, without any violation
of the energy conditions. A fundamental ingredient of traversable wormholes is
the violation of the null energy condition (NEC). However, in the brane world
models, the stress energy tensor confined on the brane, threading the wormhole,
satisfies the NEC. In conventional general relativity, wormholes existing
before inflation can be significantly enlarged by the expanding spacetime. We
investigate the evolution of an inflating wormhole in the brane world scenario,
in which the wormhole is supported by the nonlocal brane world effects. As a
first step in our study we consider the possibility of embedding a
four-dimensional brane world wormhole into a five dimensional bulk. The
conditions for the embedding are obtained by studying the junction conditions
for the wormhole geometry, as well as the full set of the five dimensional bulk
field equations. For the description of the inflation we adopt the chaotic
inflation model. We study the dynamics of the brane world wormholes during the
exponential inflation stage, and in the stage of the oscillating scalar field.
A particular exact solution corresponding to a zero redshift wormhole is also
obtained. The resulting evolution shows that while the physical and geometrical
parameters of a zero redshift wormhole decay naturally, a wormhole satisfying
some very general initial conditions could turn into a black hole, and exist
forever.Comment: 30 pages, no figures, accepted for publication in CQ
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