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Articles 1  12 of 12
FullText Articles in Physics
Introduction To Classical Field Theory, Charles G. Torre
Introduction To Classical Field Theory, Charles G. Torre
All Complete Monographs
This is an introduction to classical field theory. Topics treated include: KleinGordon field, electromagnetic field, scalar electrodynamics, Dirac field, YangMills field, gravitational field, Noether theorems relating symmetries and conservation laws, spontaneous symmetry breaking, Lagrangian and Hamiltonian formalisms.
Introduction To The Usu Library Of Solutions To The Einstein Field Equations, Ian M. Anderson, Charles G. Torre
Introduction To The Usu Library Of Solutions To The Einstein Field Equations, Ian M. Anderson, Charles G. Torre
Tutorials on... in 1 hour or less
This is a Maple worksheet providing an introduction to the USU Library of Solutions to the Einstein Field Equations. The library is part of the DifferentialGeometry software project and is a collection of symbolic data and metadata describing solutions to the Einstein equations.
The Differentialgeometry Package, Ian M. Anderson, Charles G. Torre
The Differentialgeometry Package, Ian M. Anderson, Charles G. Torre
Downloads
This is the entire DifferentialGeometry package, a zip file (DifferentialGeometry.zip) containing (1) a Maple Library file, DifferentialGeometryUSU.mla, (2) a Maple help file DifferentialGeometry.help. This is the latest version of the DifferentialGeometry software; it supersedes what is released with Maple. It has been tested on Maple versions 17, 18, 2015.
Geometrization Conditions For Perfect Fluids, Scalar Fields, And Electromagnetic Fields, Charles G. Torre, Dionisios Krongos
Geometrization Conditions For Perfect Fluids, Scalar Fields, And Electromagnetic Fields, Charles G. Torre, Dionisios Krongos
Charles G. Torre
Rainichtype conditions giving a spacetime “geometrization” of matter fields in general relativity are reviewed and extended. Three types of matter are considered: perfect fluids, scalar fields, and electromagnetic fields. Necessary and sufficient conditions on a spacetime metric for it to be part of a perfect fluid solution of the Einstein equations are given. Formulas for constructing the fluid from the metric are obtained. All fluid results hold for any spacetime dimension. Geometric conditions on a metric which are necessary and sufficient for it to define a solution of the Einsteinscalar field equations and formulas for constructing the scalar field from ...
Geometrization Conditions For Perfect Fluids, Scalar Fields, And Electromagnetic Fields, Charles G. Torre, Dionisios Krongos
Geometrization Conditions For Perfect Fluids, Scalar Fields, And Electromagnetic Fields, Charles G. Torre, Dionisios Krongos
Presentations and Publications
Rainichtype conditions giving a spacetime “geometrization” of matter fields in general relativity are reviewed and extended. Three types of matter are considered: perfect fluids, scalar fields, and elec tromagnetic fields. Necessary and sufficient conditions on a spacetime metric for it to be part of a perfect fluid solution of the Einstein equa tions are given. Formulas for constructing the fluid from the metric are obtained. All fluid results hold for any spacetime dimension. Ge ometric conditions on a metric which are necessary and sufficient for it to define a solution of the Einsteinscalar field equations and for mulas for constructing ...
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 orbital angle  the "equation ...
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 EinsteinMaxwell 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 nonnull electrovacua. Given a spacetime satisfying the conditions for a null electrovacuum, a straightforward procedure builds the null electromagnetic field from ...
RainichType Conditions For Null Electrovacuum Spacetimes Ii, Charles G. Torre
RainichType Conditions For Null Electrovacuum Spacetimes Ii, Charles G. Torre
Research Vignettes
In this second of two worksheets I continue describing local Rainichtype conditions which are necessary and sufficient for the metric to define a null electrovacuum. In other words, these conditions, which I will call the null electrovacuum conditions, guarantee the existence of a null electromagnetic field such that the metric and electromagnetic field satisfy the EinsteinMaxwell equations. When it exists, the electromagnetic field is easily constructed from the metric. In this worksheet I consider the null electrovacuum conditions which apply when a certain null geodesic congruence determined by the metric is twisting. I shall illustrate the these conditions using a ...
The Spacetime Geometry Of A Null Electromagnetic Field, Charles G. Torre
The Spacetime Geometry Of A Null Electromagnetic Field, Charles G. Torre
Presentations and Publications
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 EinsteinMaxwell 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 nonnull electrovacua. Given a spacetime satisfying the conditions for a null electrovacuum, a straightforward procedure builds the null electromagnetic field from ...
How To Find Killing Vectors, Charles G. Torre
How To Find Killing Vectors, Charles G. Torre
How to... in 10 minutes or less
We show how to compute the Lie algebra of Killing vector fields of a metric in Maple using the commands KillingVectors and LieAlgebraData. A Maple worksheet and a PDF version can be found below.
A Homogeneous Solution Of The EinsteinMaxwell Equations, Charles G. Torre
A Homogeneous Solution Of The EinsteinMaxwell Equations, Charles G. Torre
Research Vignettes
We exhibit and analyze a homogeneous spacetime whose source is a pure radiation electromagnetic field [1]. It was previously believed that this spacetime is the sole example of a homogeneous pure radiation solution of the Einstein equations which admits no electromagnetic field (see [2] and references therein). Here we correct this error in the literature by explicitly displaying the electromagnetic source. This result implies that all homogeneous pure radiation spacetimes satisfy the EinsteinMaxwell equations.
PDF and Maple worksheets can be downloaded from the links below.
How To Create A Lie Algebra, Ian M. Anderson
How To Create A Lie Algebra, Ian M. Anderson
How to... in 10 minutes or less
We show how to create a Lie algebra in Maple using three of the most common approaches: matrices, vector fields and structure equations. PDF and Maple worksheets can be downloaded from the links below.