61 research outputs found
Improved Energy-Momentum Currents in Metric-Affine Spacetime
In Minkowski spacetime it is well-known that the canonical energy-momentum
current is involved in the construction of the globally conserved currents of
energy-momentum and total angular momentum. For the construction of conserved
currents corresponding to (approximate) scale and proper conformal symmetries,
however, an improved energy-momentum current is needed. By extending the
Minkowskian framework to a genuine metric-affine spacetime, we find that the
affine Noether identities and the conformal Killing equations enforce this
improvement in a rather natural way. So far, no gravitational dynamics is
involved in our construction. The resulting dilation and proper conformal
currents are conserved provided the trace of the energy-momentum current
satisfies a (mild) scaling relation or even vanishes.Comment: 14p
ADM-like Hamiltonian formulation of gravity in the teleparallel geometry
We present a new Hamiltonian formulation of the Teleparallel Equivalent of
General Relativity (TEGR) meant to serve as the departure point for canonical
quantization of the theory. TEGR is considered here as a theory of a cotetrad
field on a spacetime. The Hamiltonian formulation is derived by means of an
ADM-like 3+1 decomposition of the field and without any gauge fixing. A
complete set of constraints on the phase space and their algebra are presented.
The formulation is described in terms of differential forms.Comment: 43 pages, LaTeX2e; the original 73 page paper arXiv:1111.5498v1 was
revised and divided into two parts. The present paper is the first part of
the original one (the second part is available as arXiv:1309.4685
Hamiltonian Analysis of Poincar\'e Gauge Theory: Higher Spin Modes
We examine several higher spin modes of the Poincar\'e gauge theory (PGT) of
gravity using the Hamiltonian analysis. The appearance of certain undesirable
effects due to non-linear constraints in the Hamiltonian analysis are used as a
test. We find that the phenomena of field activation and constraint bifurcation
both exist in the pure spin 1 and the pure spin 2 modes. The coupled spin-
and spin- modes also fail our test due to the appearance of constraint
bifurcation. The ``promising'' case in the linearized theory of PGT given by
Kuhfuss and Nitsch (KRNJ86) likewise does not pass. From this analysis of these
specific PGT modes we conclude that an examination of such nonlinear constraint
effects shows great promise as a strong test for this and other alternate
theories of gravity.Comment: 30 pages, submitted to Int. J. Mod. Phys.
Chiral fermions and torsion in the early Universe
Torsion arising from fermionic matter in the Einstein-Cartan formulation of
general relativity is considered in the context of Robertson-Walker geometries
and the early Universe. An ambiguity in the way torsion arising from hot
fermionic matter in chiral models should be implemented is highlighted and
discussed. In one interpretation, chemical potentials in chiral models can
contribute to the Friedmann equation and give a negative contribution to the
energy density.Comment: 5 pages revtex4; error in v1 corrected
On certain relationships between cosmological observables in the Einstein-Cartan gravity
We show that in the Einstein-Cartan gravity it is possible to obtain a
relation between Hubble's expansion and the global rotation (vorticity) of the
Universe. Gravitational coupling can be reduced to dimensionless quantity of
order unity, fixing the scalar mass density and the resulting negative
cosmological constant at spacelike infinity. Current estimates of the expansion
and rotation (see also astro-ph/9703082) of the Universe favour the massive
spinning particles as candidate particles for cold and hot dark matter. Nodland
and Ralston vorticity (Phys. Rev. Lett. 78 (1997) 3043) overestimates the value
favoured by the Einstein-Cartan gravity for three orders of magnitude.Comment: 7 pages, LaTeX styl
Perfect hypermomentum fluid: variational theory and equations of motion
The variational theory of the perfect hypermomentum fluid is developed. The
new type of the generalized Frenkel condition is considered. The Lagrangian
density of such fluid is stated, and the equations of motion of the fluid and
the Weyssenhoff-type evolution equation of the hypermomentum tensor are
derived. The expressions of the matter currents of the fluid (the canonical
energy-momentum 3-form, the metric stress-energy 4-form and the hypermomentum
3-form) are obtained. The Euler-type hydrodynamic equation of motion of the
perfect hypermomentum fluid is derived. It is proved that the motion of the
perfect fluid without hypermomentum in a metric-affine space coincides with the
motion of this fluid in a Riemann space.Comment: REVTEX, 23 pages, no figure
Gravitational Lorentz Force and the Description of the Gravitational Interaction
In the context of a gauge theory for the translation group, we have obtained,
for a spinless particle, a gravitational analog of the Lorentz force. Then, we
have shown that this force equation can be rewritten in terms of magnitudes
related to either the teleparallel or the riemannian structures induced in
spacetime by the presence of the gravitational field. In the first case, it
gives a force equation, with torsion playing the role of force. In the second,
it gives the usual geodesic equation of General Relativity. The main conclusion
is that scalar matter is able to feel anyone of the above spacetime geometries,
the teleparallel and the metric ones. Furthermore, both descriptions are found
to be completely equivalent in the sense that they give the same physical
trajectory for a spinless particle in a gravitational field.Comment: Equations (44)-(47) correcte
Semi-Teleparallel Theories of Gravitation
A class of theories of gravitation that naturally incorporates preferred
frames of reference is presented. The underlying space-time geometry consists
of a partial parallelization of space-time and has properties of Riemann-Cartan
as well as teleparallel geometry. Within this geometry, the kinematic
quantities of preferred frames are associated with torsion fields. Using a
variational method, it is shown in which way action functionals for this
geometry can be constructed. For a special action the field equations are
derived and the coupling to spinor fields is discussed.Comment: 14 pages, LaTe
Towards complete integrability of two dimensional Poincar\'e gauge gravity
It is shown that gravity on the line can be described by the two dimensional
(2D) Hilbert-Einstein Lagrangian supplemented by a kinetic term for the coframe
and a translational {\it boundary} term. The resulting model is equivalent to a
Yang-Mills theory of local {\it translations} and frozen Lorentz gauge degrees.
We will show that this restricted Poincar\'e gauge model in 2 dimensions is
completely integrable. {\it Exact} wave, charged black hole, and `dilaton'
solutions are then readily found. In vacuum, the integrability of the {\it
general} 2D Poincar\'e gauge theory is formally proved along the same line of
reasoning.Comment: 35 pages, report Cologne-thp-1993-H
Matrix theory of gravitation
A new classical theory of gravitation within the framework of general
relativity is presented. It is based on a matrix formulation of
four-dimensional Riemann-spaces and uses no artificial fields or adjustable
parameters. The geometrical stress-energy tensor is derived from a matrix-trace
Lagrangian, which is not equivalent to the curvature scalar R. To enable a
direct comparison with the Einstein-theory a tetrad formalism is utilized,
which shows similarities to teleparallel gravitation theories, but uses complex
tetrads. Matrix theory might solve a 27-year-old, fundamental problem of those
theories (sec. 4.1). For the standard test cases (PPN scheme,
Schwarzschild-solution) no differences to the Einstein-theory are found.
However, the matrix theory exhibits novel, interesting vacuum solutions.Comment: 24 page
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