9,159 research outputs found
Gauge-Invariant Localization of Infinitely Many Gravitational Energies from all Possible Auxiliary Structures, Or, Why Pseudotensors are Okay
The problem of finding a covariant expression for the distribution and
conservation of gravitational energy-momentum dates to the 1910s. A suitably
covariant infinite-component localization is displayed, reflecting Bergmann's
realization that there are infinitely many conserved gravitational
energy-momenta. Initially use is made of a flat background metric or connection
(or rather, all of them), because the desired gauge invariance properties are
obvious. Partial gauge-fixing then yields an appropriate covariant quantity
without any background metric or connection; one version is the collection of
pseudotensors of a given type, such as the Einstein pseudotensor, in_every_
coordinate system. This solution to the gauge covariance problem is easily
adapted to any pseudotensorial expression or to any tensorial expression built
with a background metric or connection. Thus the specific functional form can
be chosen on technical grounds such as relating to Noether's theorem and
yielding expected values of conserved quantities in certain contexts and then
rendered covariant using the procedure described here. The application to
angular momentum localization is straightforward. Traditional objections to
pseudotensors are based largely on the false assumption that there is only one
gravitational energy rather than infinitely many.Comment: Proceedings of the DPF-2009 Conference, Detroit, MI, July 27-31, 200
The Relevance of Irrelevance: Absolute Objects and the Jones-Geroch Dust Velocity Counterexample, with a Note on Spinors
James L. Anderson analyzed the conceptual novelty of Einstein's theory of gravity as its lack of ``absolute objects.'' Michael Friedman's related concept of absolute objects has been criticized by Roger Jones and Robert Geroch for implausibly admitting as absolute the timelike 4-velocity field of dust in cosmological models in Einstein's theory. Using Nathan Rosen's action principle, I complete Anna Maidens's argument that the Jones-Geroch problem is not solved by requiring that absolute objects not be varied. Recalling Anderson's proscription of (globally) ``irrelevant'' variables that do no work (anywhere in any model), I generalize that proscription to locally irrelevant variables that do no work in some places in some models. This move vindicates Friedman's intuitions and removes the Jones-Geroch counterexample: some regions of some models of gravity with dust are dust-free, and there is no good reason to have a timelike dust 4-velocity vector there. Eliminating the irrelevant timelike vctors keeps the dust 4-velocity from counting as absolute by spoiling its neighborhood-by-neighborhood diffeomorphic equivalence to (1,0,0,0). A more fundamental Gerochian timelike vector field presents itself in gravity with spinors in the standard orthonormal tetrad formalism, though eliminating irrelevant fields might solve this problem as well
Airoscope telemetry system
The AIROscope (Ames Infrared Observatory telescope) telemetry system is described from signal conditioning on the gondola to display and storage at the ground station. All analog and digital data from the systems and experiments on the gondola go to a PCM encoder which formats the data into 10-bit words. Therefore, 0.1-percent resolution is inherently available for experimental data. The coded bit stream directly modulates the carrier of the FM transmitter. To insure reliable transmission over a 650-km range an 11-watt FM transmitter operating at 1483.5 MHz is used on the gondola. Modulation is narrow band FM with a maximum deviation of plus or minus 500 kHz. The maximum modulation frequency is determined by the data bit rate which could be as high as 500 kbps. Presently, a rate of 20.48 kbps is used. The ground station receiving system includes a steerable antenna (19-db gain), preamplifier (21-db gain) and receiver. All data are recorded on a tape recorder. The recorded signal then can be played back through the PCM decommutator unit at a later time for detailed data analysis by the experimenter
Youth gangs, sexual violence and sexual exploitation: a scoping exercise for the Office of the Children's Commissioner for England
This report presents the findings of a scoping exercise on the issue of youth gangs, sexual violence and sexual exploitation, derived from key informant interviews and a literature review
Null Cones in Lorentz-Covariant General Relativity
The oft-neglected issue of the causal structure in the flat spacetime
approach to Einstein's theory of gravity is considered. Consistency requires
that the flat metric's null cone be respected, but this does not happen
automatically. After reviewing the history of this problem, we introduce a
generalized eigenvector formalism to give a kinematic description of the
relation between the two null cones, based on the Segre' classification of
symmetric rank 2 tensors with respect to a Lorentzian metric. Then we propose a
method to enforce special relativistic causality by using the naive gauge
freedom to restrict the configuration space suitably. A set of new variables
just covers this smaller configuration space and respects the flat metric's
null cone automatically. In this smaller space, gauge transformations do not
form a group, but only a groupoid. Respecting the flat metric's null cone
ensures that the spacetime is globally hyperbolic, indicating that the Hawking
black hole information loss paradox does not arise.Comment: groupoid nature of gauge transformations explained; shortened, new
references, 102 page
Null Cones and Einstein's Equations in Minkowski Spacetime
If Einstein's equations are to describe a field theory of gravity in
Minkowski spacetime, then causality requires that the effective curved metric
must respect the flat background metric's null cone. The kinematical problem is
solved using a generalized eigenvector formalism based on the Segr\'{e}
classification of symmetric rank 2 tensors with respect to a Lorentzian metric.
Securing the correct relationship between the two null cones dynamically
plausibly is achieved using the naive gauge freedom. New variables tied to the
generalized eigenvector formalism reduce the configuration space to the
causality-respecting part. In this smaller space, gauge transformations do not
form a group, but only a groupoid. The flat metric removes the difficulty of
defining equal-time commutation relations in quantum gravity and guarantees
global hyperbolicity
- …