459 research outputs found
A Quadratic Spinor Lagrangian for General Relativity
We present a new finite action for Einstein gravity in which the Lagrangian
is quadratic in the covariant derivative of a spinor field. Via a new
spinor-curvature identity, it is related to the standard Einstein-Hilbert
Lagrangian by a total differential term. The corresponding Hamiltonian, like
the one associated with the Witten positive energy proof is fully
four-covariant. It defines quasi-local energy-momentum and can be reduced to
the one in our recent positive energy proof. (Fourth Prize, 1994 Gravity
Research Foundation Essay.)Comment: 5 pages (Plain TeX), NCU-GR-94-QSL
Another positivity proof and gravitational energy localizations
Two locally positive expressions for the gravitational Hamiltonian, one using
4-spinors the other special orthonormal frames, are reviewed. A new quadratic
3-spinor-curvature identity is used to obtain another positive expression for
the Hamiltonian and thereby a localization of gravitational energy and positive
energy proof. These new results provide a link between the other two methods.
Localization and prospects for quasi-localization are discussed.Comment: 14 pages REVTe
Quasi-local Energy for Spherically Symmetric Spacetimes
We present two complementary approaches for determining the reference for the
covariant Hamiltonian boundary term quasi-local energy and test them on
spherically symmetric spacetimes. On the one hand, we isometrically match the
2-surface and extremize the energy. This can be done in two ways, which we call
programs I (without constraint) and II (with additional constraints). On the
other hand, we match the orthonormal 4-frames of the dynamic and the reference
spacetimes. Then, if we further specify the observer by requiring the reference
displacement to be the timelike Killing vector of the reference, the result is
the same as program I, and the energy can be positive, zero, or even negative.
If, instead, we require that the Lie derivatives of the two-area along the
displacement vector in both the dynamic and reference spacetimes to be the
same, the result is the same as program II, and it satisfies the usual
criteria: the energies are non-negative and vanish only for Minkowski (or
anti-de Sitter) spacetime.Comment: 16 pages, no figure
Ashtekar Variables in Classical General Realtivity
This paper contains an introduction into Ashtekar's reformulation of General
Relativity in terms of connection variables. To appear in "Canonical Gravity -
From Classical to Quantum", ed. by J. Ehlers and H. Friedrich, Springer Verlag
(1994).Comment: 31 Pages, Plain-Tex; Further comments were added, minor grammatical
changes made and typos correcte
Quasi-local energy-momentum and energy flux at null infinity
The null infinity limit of the gravitational energy-momentum and energy flux
determined by the covariant Hamiltonian quasi-local expressions is evaluated
using the NP spin coefficients. The reference contribution is considered by
three different embedding approaches. All of them give the expected Bondi
energy and energy flux.Comment: 14 pages, accepted by Phys.Rev.
On the energy of homogeneous cosmologies
An energy for the homogeneous cosmological models is presented. More
specifically, using an appropriate natural prescription, we find the energy
within any region with any gravitational source for a large class of gravity
theories--namely those with a tetrad description--for all 9 Bianchi types. Our
energy is given by the value of the Hamiltonian with homogeneous boundary
conditions; this value vanishes for all regions in all Bianchi class A models,
and it does not vanish for any class B model. This is so not only for
Einstein's general relativity but, moreover, for the whole 3-parameter class of
tetrad-teleparallel theories. For the physically favored one parameter
subclass, which includes the teleparallel equivalent of Einstein's theory as an
important special case, the energy for all class B models is, contrary to
expectation, negative.Comment: 11 pages, reformated with minor change
How do novice and improver walkers move in their home environments? An open-sourced infant’s gait video analysis
Objective
Natural independent walking mostly occurs during infant´s everyday explorations of their home environment. Gait characteristics of infant walkers at different developmental stages exist in literature, however, data has been only collected in laboratory environments, which may reduce gait variability, therefore mask differences between developmental stages of natural gait. The aim of the study was to provide the first data set of temporal and functional gait characteristics of novice and improver infant walkers in familiar environment conditions in their home. We hypothesised that familiar environment conditions may effectively demonstrate natural gait characteristics and real differences in gait variables differing between 2 groups of developing infant walkers.
Methods
In a cross-sectional design; we used open-source videos of infants in their home environments: twenty videos of 10 novice (5 girls, 5 boys, 7–12 months) and 10 improver (4 girls, 6 boys, 8–13 months) walkers were chosen from an open-source website. 2-D video gait analysis was undertaken for these parameters: falls frequency, frequency of stops, gait cadence, and time of stance phase, swing phase, and double support. Between groups comparison for novice versus improver was investigated by Mann-Whitney U tests (p ≤ 0.05) with determination of effect size of Pearson r correlation.
Results
Statistically significant differences between groups with large effect sizes were found for these parameters: falls frequency (p = 0.01, r = 0.56); cadence (p = 0.01, r = 0.57); stance phase duration of right leg (p < 0.01, r = 0.63); stance phase duration of left leg (p = 0.01, r = 0.56); and double support phase duration (p < 0.01, r = 0.69). Novices scored higher in comparison with improver walkers in all the parameters except cadence.
Conclusions
This study presents the first data set of functional and temporal gait parameters of novice and improver infant walkers in their home environments. As an addition to recent research, novice infants walk with lower cadence and higher falls frequency, stance phase time and double support in their familiar environments. With increasing experiences, infant´s cadence increases while the other parameters decrease
The Hamiltonian boundary term and quasi-local energy flux
The Hamiltonian for a gravitating region includes a boundary term which
determines not only the quasi-local values but also, via the boundary variation
principle, the boundary conditions. Using our covariant Hamiltonian formalism,
we found four particular quasi-local energy-momentum boundary term expressions;
each corresponds to a physically distinct and geometrically clear boundary
condition. Here, from a consideration of the asymptotics, we show how a
fundamental Hamiltonian identity naturally leads to the associated quasi-local
energy flux expressions. For electromagnetism one of the four is distinguished:
the only one which is gauge invariant; it gives the familiar energy density and
Poynting flux. For Einstein's general relativity two different boundary
condition choices correspond to quasi-local expressions which asymptotically
give the ADM energy, the Trautman-Bondi energy and, moreover, an associated
energy flux (both outgoing and incoming). Again there is a distinguished
expression: the one which is covariant.Comment: 12 pages, no figures, revtex
Mass and Spin of Poincare Gauge Theory
We discuss two expressions for the conserved quantities (energy momentum and
angular momentum) of the Poincar\'e Gauge Theory. We show, that the variations
of the Hamiltonians, of which the expressions are the respective boundary
terms, are well defined, if we choose an appropriate phase space for asymptotic
flat gravitating systems. Furthermore, we compare the expressions with others,
known from the literature.Comment: 16 pages, plain-tex; to be published in Gen. Rel. Gra
Dirac spinor fields in the teleparallel gravity: comment on "Metric-affine approach to teleparallel gravity"
We show that the coupling of a Dirac spinor field with the gravitational
field in the teleparallel equivalent of general relativity is consistent. For
an arbitrary SO(3,1) connection there are two possibilities for the coupling of
the spinor field with the gravitational field. The problems of consistency
raised by Y. N. Obukhov and J. G. Pereira in the paper {\it Metric-affine
approach to teleparallel gravity} [gr-qc/0212080] take place only in the
framework of one particular coupling. By adopting an alternative coupling the
consistency problem disappears.Comment: 8 pages, Latex file, no figures, to appear in the Phys. Rev. D as a
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