802 research outputs found
Some Spinor-Curvature Identities
We describe a class of spinor-curvature identities which exist for Riemannian
or Riemann-Cartan geometries. Each identity relates an expression quadratic in
the covariant derivative of a spinor field with an expression linear in the
curvature plus an exact differential. Certain special cases in 3 and 4
dimensions which have been or could be used in applications to General
Relativity are noted.Comment: 5 pages Plain TeX, NCU-GR-93-SSC
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
Ashtekar's New Variables and Positive Energy
We discuss earlier unsuccessful attempts to formulate a positive
gravitational energy proof in terms of the New Variables of Ashtekar. We also
point out the difficulties of a Witten spinor type proof. We then use the
special orthonormal frame gauge conditions to obtain a locally positive
expression for the New Variables Hamiltonian and thereby a ``localization'' of
gravitational energy as well as a positive energy proof.Comment: 12 pages Plain Te
Lagrange formulation of the symmetric teleparallel gravity
We develop a symmetric teleparallel gravity model in a space-time with only
the non-metricity is nonzero, in terms of a Lagrangian quadratic in the
non-metricity tensor. We present a detailed discussion of the variations that
may be used for any gravitational formulation. We seek Schwarzschild-type
solutions because of its observational significance and obtain a class of
solutions that includes Schwarzschild-type, Schwarzschild-de Sitter-type and
Reissner-Nordstr\"{o}m-type solutions for certain values of the parameters. We
also discuss the physical relevance of these solutions.Comment: Corrected typos, Accepted for publication in IJMP-
Sensitivity analysis by the adjoint chemistry transport model DRAISfor an episode in the Berlin Ozone (BERLIOZ) experiment
International audienceThe Berlin Ozone Experiment (BERLIOZ) was carried out in summer 1998. One of its purposes was the evaluation of Chemistry Transport Models (CTM). CTM KAMM/DRAIS was one of the models considered. The data of 20 July were selected for evaluation. On that day, a pronounced ozone plume developed downwind of the city. Evaluation showed that the KAMM/DRAIS model is able to reproduce the meteorological and ozone data observed, except at farther distances (60?80 km) downwind of the city. In that region, the DRAIS model underestimates the measured ozone concentrations by 10?15 ppb, approximately. Therefore, this study was conducted to detect possible reasons for this deviation. A comprehensive sensitivity analysis was carried out to determine the most relevant model parameters. The adjoint DRAIS model was developed for this purpose, because for this study the application of this model is the most effective method of calculating the sensitivities. The least squares of the measured and simulated ozone concentrations between 08:00 UTC and 16:00 UTC at two stations 30 km and 70 km downwind of the city centre were chosen as distance function. The model parameters considered in this study are the complete set of initial and boundary species concentrations, emissions, and reaction rates, respectively. A sensitivity ranking showing the relevance of the individual parameters in the set is determined for each parameter set. In order to find out which modification in the parameter sets most reduces the cost function, simplified 4-D data assimilation was carried out. The result of this data assimilation shows that modifications of the reaction rates provide the best agreement between the measured and the simulated ozone concentrations at both stations. However, the modified reaction rates seem to be unrealistic for the whole simulation period. Therefore, the good agreement should not be overestimated. The agreement is still acceptable when the parameters in the other sets are modified together. The investigation demonstrates that an analysis of this type can help to explain inconsistencies between observations and simulations. But in the case considered here the inconsistencies cannot be explained by an error in only one parameter set
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 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
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