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Full-Text Articles in Physics

Introduction To The Usu Library Of Solutions To The Einstein Field Equations, Ian M. Anderson, Charles G. Torre Dec 2017

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 Jan 2016

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.

Installation instructions


Rainich-Type Conditions For Perfect Fluid Spacetimes, Dionisios Krongos, Charles G. Torre Dec 2014

Rainich-Type Conditions For Perfect Fluid Spacetimes, Dionisios Krongos, Charles G. Torre

Research Vignettes

In this worksheet we describe and illustrate a relatively simple set of new Rainich-type conditions on an n-dimensional spacetime which are necessary and sufficient for it to define a perfect fluid solution of the Einstein field equations. Procedures are provided which implement these Rainich-type conditions and which reconstruct the perfect fluid from the metric. These results provide an example of the idea of geometrization of matter fields in general relativity, which is a purely geometrical characterization of matter fields via the Einstein field equations.


Rainich-Type Conditions For Null Electrovacuum Spacetimes Ii, Charles G. Torre Oct 2013

Rainich-Type Conditions For Null Electrovacuum Spacetimes Ii, Charles G. Torre

Research Vignettes

In this second of two worksheets I continue describing local Rainich-type 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 Einstein-Maxwell 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 ...


How To Find Killing Vectors, Charles G. Torre Mar 2013

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.


How To Create A Two-Component Spinor, Charles G. Torre Oct 2012

How To Create A Two-Component Spinor, Charles G. Torre

How to... in 10 minutes or less

Let (M, g) be a spacetime, i.e., a 4-dimensional manifold M and Lorentz signature metric g. The key ingredients needed for constructing spinor fields on the spacetime are: a complex vector bundle E -> M ; an orthonormal frame on TM ; and a solder form relating sections of E to sections of TM (and tensor products thereof). We show how to create a two-component spinor field on the Schwarzschild spacetime using the DifferentialGeometry package in Maple. PDF and Maple worksheets can be downloaded from the links below.


A Homogeneous Solution Of The Einstein-Maxwell Equations, Charles G. Torre Jul 2012

A Homogeneous Solution Of The Einstein-Maxwell 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 Einstein-Maxwell equations.

PDF and Maple worksheets can be downloaded from the links below.


How To Create A Lie Algebra, Ian M. Anderson Jul 2012

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.


Lettau Affect Colloquium: Or Seeing Natural Philosophy With Len, L. F. Hall Feb 2011

Lettau Affect Colloquium: Or Seeing Natural Philosophy With Len, L. F. Hall

Leonard F. Hall

I was a Senior-Grad student in the Department of Meteorology at the University of Wisconsin at Madison on 19 December 1969. After purchasing a camera to photograph motorcycle trips, I returned to the 13th floor of the Meteorology and Space Science building in time to attend the annual slide show presented by Professor Heinz H. Lettau. Slides were collected from department members to augment his own and Dr. Lettau organized and presented the set. It was a feast of previously unnoticed phenomena that enriched my life. This presentation of photos and composites celebrates a rich contribution of a Doktor Vater ...


Lettau Affect Colloquium: Or Seeing Natural Philosophy With Len, Leonard Hall Feb 2011

Lettau Affect Colloquium: Or Seeing Natural Philosophy With Len, Leonard Hall

All Physics Faculty Publications

No abstract provided.


Phys 6210 - Quantum Mechanics, Spring 2007, Charles G. Torre Jan 2007

Phys 6210 - Quantum Mechanics, Spring 2007, Charles G. Torre

Physics - OCW

After completing this course you should (1) have a working knowledge of the foundations, techniques and key results of quantum mechanics; (2) be able to comprehend basic quantum mechanical applications at the research level, e.g., in research articles; (3) be able to competently explain/teach these topics to others; (4) be able to teach yourself any other related quantum mechanics material as you need it.