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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Gauge Theories Of General Relativity, James Thomas Wheeler
Gauge Theories Of General Relativity, James Thomas Wheeler
James Thomas Wheeler
General relativity can be seen as a gauge theory of the Lorentz, Poincaré, Weyl, de Sitter, or conformal groups. In most of these, there is little or no difference from the standard formulation in Riemannian geometry, but the higher symmetries — de Sitter and conformal — introduce new features and explain old ones. The potential presence of a cosmological constant, the spacetime metric, cosmological dust, symplectic structure, Kähler structure and even the existence of a timelike direction can all be seen to arise from the underlying group structure.
Weyl Gravity As General Relativity, James Thomas Wheeler
Weyl Gravity As General Relativity, James Thomas Wheeler
James Thomas Wheeler
When the full connection of Weyl conformal gravity is varied instead of just the metric, the resulting vacuum field equations reduce to the vacuum Einstein equation, up to the choice of local units, if and only if the torsion vanishes. This result differs strongly from the usual fourth-order formulation of Weyl gravity.
Perihelion Precession In General Relativity, Charles G. Torre
Perihelion Precession In General Relativity, Charles G. Torre
Charles G. Torre
This is a Maple worksheet providing a relatively quick and informal sketch of a demonstration that general relativistic corrections to the bound Kepler orbits introduce a perihelion precession. Any decent textbook will derive this result. My analysis aligns with that found in the old text "Introduction to General Relativity", by Adler, Bazin and Schiffer. The plan of the analysis is as follows. * Model the planetary orbits as geodesics in the (exterior) Schwarzschild spacetime. * Compute the geodesic equations. * Simplify them using symmetries and first integrals. * Isolate the differential equation expressing the radial coordinate as a function of …
The Spacetime Geometry Of A Null Electromagnetic Field, Charles G. Torre
The Spacetime Geometry Of A Null Electromagnetic Field, Charles G. Torre
Charles G. Torre
We give a set of local geometric conditions on a spacetime metric which are necessary and sufficient for it to be a null electrovacuum, that is, the metric is part of a solution to the Einstein-Maxwell equations with a null electromagnetic field. These conditions are restrictions on a null congruence canonically constructed from the spacetime metric, and can involve up to five derivatives of the metric. The null electrovacuum conditions are counterparts of the Rainich conditions, which geometrically characterize non-null electrovacua. Given a spacetime satisfying the conditions for a null electrovacuum, a straightforward procedure builds the null electromagnetic field from …
Paleolimnological Analysis Of The History Of Metals Contamination In The Great Salt Lake, Utah, Wayne A. Wurtsbaugh, Katrina Moser, Peter R. Leavitt
Paleolimnological Analysis Of The History Of Metals Contamination In The Great Salt Lake, Utah, Wayne A. Wurtsbaugh, Katrina Moser, Peter R. Leavitt
Wayne A. Wurtsbaugh
Three sediment cores from the Great Salt Lake were analyzed to determine the magnitude and timing for the deposition of 21 metal contaminants. In the main lake (Gilbert Bay) concentrations of copper, lead, zinc, cadmium, silver, molybdenum, tin, mercury and others began increasing in the sediments in the late 1800s or early 1900s and peaked in the 1950s. These increases were coincident with increases in mining and smelting activities for these metals in Utah. Contamination indices in the 1950s were 20-60 fold above background concentrations for silver, copper, lead and molybdenum, and <15-fold for most other metals. Since the 1950s, concentrations of most metals in the sediments have decreased 2-5 fold coincident with decreases in mining and improved smelting technologies. Nevertheless concentrations for many metals in surficial sediments are still above acceptable criteria established for freshwater ecosystems. In contrast to most metals, concentrations of selenium and arsenic were stable or increasing slightly in the Gilbert Bay sediments. In a coring site located in Farmington Bay near an EPA Superfund Site discharge canal, concentrations of metals were high and showed no indication of decreasing in more recent sediments. Surficial sediments from additional sites in the Great Salt Lake indicated that metals were more concentrated towards the southern end of the lake where the primary sources of contamination were located.