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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 …