53 research outputs found
Spin and Rotation in General Relativity
Rapporteur's Introduction to the GT8 session of the Ninth Marcel Grossmann
Meeting (Rome, 2000); to appear in the Proceedings.Comment: LaTeX file, no figures, 15 page
An assessment of Evans' unified field theory I
Evans developed a classical unified field theory of gravitation and
electromagnetism on the background of a spacetime obeying a Riemann-Cartan
geometry. This geometry can be characterized by an orthonormal coframe theta
and a (metric compatible) Lorentz connection Gamma. These two potentials yield
the field strengths torsion T and curvature R. Evans tried to infuse
electromagnetic properties into this geometrical framework by putting the
coframe theta to be proportional to four extended electromagnetic potentials A;
these are assumed to encompass the conventional Maxwellian potential in a
suitable limit. The viable Einstein-Cartan(-Sciama-Kibble) theory of gravity
was adopted by Evans to describe the gravitational sector of his theory.
Including also the results of an accompanying paper by Obukhov and the author,
we show that Evans' ansatz for electromagnetism is untenable beyond repair both
from a geometrical as well as from a physical point of view. As a consequence,
his unified theory is obsolete.Comment: 39 pages of latex, modified because of referee report, mistakes and
typos removed, partly reformulated, taken care of M.W.Evans' rebutta
Gravitational Energy of Kerr and Kerr Anti-de Sitter Space-times in the Teleparallel Geometry
In the context of the Hamiltonian formulation of the teleparallel equivalent
of general relativity we compute the gravitational energy of Kerr and Kerr
Anti-de Sitter (Kerr-AdS) space-times. The present calculation is carried out
by means of an expression for the energy of the gravitational field that
naturally arises from the integral form of the constraint equations of the
formalism. In each case, the energy is exactly computed for finite and
arbitrary spacelike two-spheres, without any restriction on the metric
parameters. In particular, we evaluate the energy at the outer event horizon of
the black holes.Comment: 11 pages, 1 figure, to appear in JHEP11(2003)00
Cartan's spiral staircase in physics and, in particular, in the gauge theory of dislocations
In 1922, Cartan introduced in differential geometry, besides the Riemannian
curvature, the new concept of torsion. He visualized a homogeneous and
isotropic distribution of torsion in three dimensions (3d) by the "helical
staircase", which he constructed by starting from a 3d Euclidean space and by
defining a new connection via helical motions. We describe this geometric
procedure in detail and define the corresponding connection and the torsion.
The interdisciplinary nature of this subject is already evident from Cartan's
discussion, since he argued - but never proved - that the helical staircase
should correspond to a continuum with constant pressure and constant internal
torque. We discuss where in physics the helical staircase is realized: (i) In
the continuum mechanics of Cosserat media, (ii) in (fairly speculative) 3d
theories of gravity, namely a) in 3d Einstein-Cartan gravity - this is Cartan's
case of constant pressure and constant intrinsic torque - and b) in 3d Poincare
gauge theory with the Mielke-Baekler Lagrangian, and, eventually, (iii) in the
gauge field theory of dislocations of Lazar et al., as we prove for the first
time by arranging a suitable distribution of screw dislocations. Our main
emphasis is on the discussion of dislocation field theory.Comment: 31 pages, 8 figure
Avoiding degenerate coframes in an affine gauge approach to quantum gravity
In quantum models of gravity, it is surmized that configurations with
degenerate coframes could occur during topology change of the underlying
spacetime structure. However, the coframe is not the true Yang--Mills type
gauge field of the translations, since it lacks the inhomogeneous gradient term
in the gauge transformations. By explicitly restoring this ``hidden" piece
within the framework of the affine gauge approach to gravity, one can avoid the
metric or coframe degeneracy which would otherwise interfere with the
integrations within the path integral. This is an important advantage for
quantization.Comment: 14 pages, Preprint Cologne-thp-1993-H
Gravitation, electromagnetism and cosmological constant in purely affine gravity
The Ferraris-Kijowski purely affine Lagrangian for the electromagnetic field,
that has the form of the Maxwell Lagrangian with the metric tensor replaced by
the symmetrized Ricci tensor, is dynamically equivalent to the metric
Einstein-Maxwell Lagrangian, except the zero-field limit, for which the metric
tensor is not well-defined. This feature indicates that, for the
Ferraris-Kijowski model to be physical, there must exist a background field
that depends on the Ricci tensor. The simplest possibility, supported by recent
astronomical observations, is the cosmological constant, generated in the
purely affine formulation of gravity by the Eddington Lagrangian. In this paper
we combine the electromagnetic field and the cosmological constant in the
purely affine formulation. We show that the sum of the two affine (Eddington
and Ferraris-Kijowski) Lagrangians is dynamically inequivalent to the sum of
the analogous (CDM and Einstein-Maxwell) Lagrangians in the
metric-affine/metric formulation. We also show that such a construction is
valid, like the affine Einstein-Born-Infeld formulation, only for weak
electromagnetic fields, on the order of the magnetic field in outer space of
the Solar System. Therefore the purely affine formulation that combines
gravity, electromagnetism and cosmological constant cannot be a simple sum of
affine terms corresponding separately to these fields. A quite complicated form
of the affine equivalent of the metric Einstein-Maxwell- Lagrangian
suggests that Nature can be described by a simpler affine Lagrangian, leading
to modifications of the Einstein-Maxwell-CDM theory for
electromagnetic fields that contribute to the spacetime curvature on the same
order as the cosmological constant.Comment: 17 pages, extended and combined with gr-qc/0612193; published versio
Teleparallel Version of the Levi-Civita Vacuum Solutions and their Energy Contents
In this paper, we find the teleparallel version of the Levi-Civita metric and
obtain tetrad and the torsion fields. The tensor, vector and the axial-vector
parts of the torsion tensor are evaluated. It is found that the vector part
lies along the radial direction only while the axial-vector vanishes everywhere
because the metric is diagonal. Further, we use the teleparallel version of
Mller, Einstein, Landau-Lifshitz and Bergmann-Thomson prescriptions
to find the energy-momentum distribution of this metric and compare the results
with those already found in General Relativity. It is worth mentioning here
that momentum is constant in both the theories for all the prescriptions. The
energy in teleparallel theory is equal to the corresponding energy in GR only
in Mller prescription for the remaining prescriptions, the energy do
not agree in both theories. We also conclude that Mller's
energy-momentum distribution is independent of the coupling constant
in the teleparallel theory.Comment: 15 pages, accepted for publication in Canadian J. Physic
Erratum to: An Entropy Functional for Riemann-Cartan Space-Times
We correct the entropy functional constructed in Int. J. Theor. Phys. 51:362
(2012). The 'on-shell' functional one obtains from this correct functional
possesses a holographic structure without imposing any constraint on the
spin-angular momentum tensor of matter, in contrast to the conclusion made in
the above paper.Comment: 15 pages. These are the preprints of the original paper and its
erratum published in Int. J. Theor. Phy
Three-nucleon mechanisms in photoreactions
The C reaction has been measured for
E=150-800 MeV in the first study of this reaction in a target
heavier than He. The experimental data are compared to a microscopic many
body calculation. The model, which predicts that the largest contribution to
the reaction arises from final state interactions following an initial pion
production process, overestimates the measured cross sections and there are
strong indications that the overestimate arises in this two-step process. The
selection of suitable kinematic conditions strongly suppresses this two-step
contribution leaving cross sections in which up to half the yield is predicted
to arise from the absorption of the photon on three interacting nucleons and
which agree with the model. The results indicate measurements on
nuclei may be a valuable tool for obtaining information on the nuclear
three-body interaction.Comment: 5 pages, 3 figure
Thermodynamic Gravity and the Schrodinger Equation
We adopt a 'thermodynamical' formulation of Mach's principle that the rest
mass of a particle in the Universe is a measure of its long-range collective
interactions with all other particles inside the horizon. We consider all
particles in the Universe as a 'gravitationally entangled' statistical ensemble
and apply the approach of classical statistical mechanics to it. It is shown
that both the Schrodinger equation and the Planck constant can be derived
within this Machian model of the universe. The appearance of probabilities,
complex wave functions, and quantization conditions is related to the
discreetness and finiteness of the Machian ensemble.Comment: Minor corrections, the version accepted by Int. J. Theor. Phy
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