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Articles 1 - 19 of 19
Full-Text Articles in Cosmology, Relativity, and Gravity
A New Non-Inheriting Homogeneous Solution Of The Einstein-Maxwell Equations With Cosmological Term, Charles G. Torre
A New Non-Inheriting Homogeneous Solution Of The Einstein-Maxwell Equations With Cosmological Term, Charles G. Torre
Research Vignettes
No abstract provided.
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, (3) a Maple Library file, DGApplicatons.mla. This is the latest version of the DifferentialGeometry software; it supersedes what is released with Maple.
What's New In Differentialgeometry Release Dg2022, Ian M. Anderson, Charles G. Torre
What's New In Differentialgeometry Release Dg2022, Ian M. Anderson, Charles G. Torre
Tutorials on... in 1 hour or less
This Maple worksheet demonstrates the salient new features and functionalities of the 2022 release of the DifferentialGeometry software package.
Spacetime Groups, Ian M. Anderson, Charles G. Torre
Spacetime Groups, Ian M. Anderson, Charles G. Torre
Publications
A spacetime group is a connected 4-dimensional Lie group G endowed with a left invariant Lorentz metric h and such that the connected component of the isometry group of h is G itself. The Newman-Penrose formalism is used to give an algebraic classification of spacetime groups, that is, we determine a complete list of inequivalent spacetime Lie algebras, which are pairs (g,η), with g being a 4-dimensional Lie algebra and η being a Lorentzian inner product on g. A full analysis of the equivalence problem for spacetime Lie algebras is given which leads to a completely algorithmic solution to the …
How To Make Tetrads, Charles G. Torre
How To Make Tetrads, Charles G. Torre
How to... in 10 minutes or less
This is a worksheet which demonstrates tools for creating orthonormal and null tetrads for a given spacetime.
Symmetric Criticality In General Relativity, Charles G. Torre
Symmetric Criticality In General Relativity, Charles G. Torre
Research Vignettes
In this worksheet I explore the local Lagrangian version of the Principle of Symmetric Criticality (PSC) due to Anderson, Fels, and Torre], which asserts the commutativity of the processes (i) of symmetry reduction (for finding group-invariant fields) and (ii) forming Euler-Lagrange equations. There are two obstructions to PSC, which I will call the Lie algebra obstruction and the isotropy obstruction. In this worksheet I will illustrate these obstructions in the General Theory of Relativity.
Examples Of The Birkhoff Theorem And Its Generalizations, Charles G. Torre
Examples Of The Birkhoff Theorem And Its Generalizations, Charles G. Torre
Tutorials on... in 1 hour or less
In this worksheet I demonstrate three versions of Birkhoff's theorem, which is a characterization of spherically symmetric solutions of the Einstein equations. The three versions considered here correspond to taking the "Einstein equations" to be: (1) the vacuum Einstein equations; (2) the Einstein equations with a cosmological constant (3) the Einstein-Maxwell equations. I will restrict my attention to 4-dimensional spacetimes.
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.
Fermi-Lat Daily Monitoring Observations Of The Microquasar Cygnus X-1, Austin P. Waldron, Stephen R. Hood, Arash Bodaghee
Fermi-Lat Daily Monitoring Observations Of The Microquasar Cygnus X-1, Austin P. Waldron, Stephen R. Hood, Arash Bodaghee
Georgia College Student Research Events
Detection of gamma-ray emission from microquasars is important for understanding particle acceleration in the jet, and for constraining leptonic/hadronic emission models. We present a continuation of a 1-d likelihood analysis on gamma-ray observations by Fermi-LAT (0.1-10 GeV) of the accreting black hole candidate Cygnus X-1. Combining this gamma-ray data with available X-ray monitoring data from Swift and MAXI allowed us to reveal over a dozen days (in 2008-2016) during which Cyg X-1 displayed low-significance (3-4 sigma) excesses, many of which were contemporaneous with apparent transitions in the X-rays.
Perihelion Precession In The General Theory Of Relativity, Charles G. Torre
Perihelion Precession In The General Theory Of Relativity, Charles G. Torre
Tutorials on... in 1 hour or less
This is 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 on the general theory of relativity will derive this result. My analysis aligns with that found in the good old text "Introduction to General Relativity", by Adler, Bazin and Schiffer.
The Kretschmann Scalar, Charles G. Torre
The Kretschmann Scalar, Charles G. Torre
How to... in 10 minutes or less
On a pseudo-Riemannian manifold with metric g, the "Kretschmann scalar" is a quadratic scalar invariant of the Riemann R tensor of g, defined by contracting all indices with g. In this worksheet we show how to calculate the Kretschmann scalar from a metric.
Differentialgeometry In Brno, Ian M. Anderson
Differentialgeometry In Brno, Ian M. Anderson
Presentations
This page will provide files supporting Ian Anderson's presentations in Brno, December 2015. The files can be found and downloaded from "Additional Files", below.
The files include:
(1) DifferentialGeometryUSU.mla: This is the Maple Library Archive file which provides all the DifferentialGeometry functionality. Here are Installation Instructions.
(2) DifferentialGeometry.help : this is the latest version of the DifferentialGeometry documentation. Copy this file to the same directory used for DifferentialGeometryUSU.mla (from step (1)).
Gravitational Waves: A New Window Into The Cosmos, Jeffrey S. Hazboun
Gravitational Waves: A New Window Into The Cosmos, Jeffrey S. Hazboun
Jeffrey Hazboun
No abstract provided.
Rainich-Type Conditions For Perfect Fluid Spacetimes, Dionisios Krongos, Charles G. Torre
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.
A Comparison Of X-Ray And Optical Emission In Cassiopeia A, Daniel J. Patnaude, Robert A. Fesen
A Comparison Of X-Ray And Optical Emission In Cassiopeia A, Daniel J. Patnaude, Robert A. Fesen
Dartmouth Scholarship
Broadband optical and narrowband Si XIII X-ray images of the young Galactic supernova remnant Cassiopeia A (Cas A) obtained over several decades are used to investigate spatial and temporal emission correlations on both large and small angular scales. The data examined consist of optical and near infrared ground-based and Hubble Space Telescope images taken between 1951 and 2011, and X-ray images from Einstein, ROSAT, and Chandra taken between 1979 and 2013. We find weak spatial correlations between the remnant’s X-ray and optical emission features on large scales, but several cases of good optical/X-ray correlations on small scales for features which …
Rainich-Type Conditions For Null Electrovacuum Spacetimes Ii, Charles G. Torre
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 …
Gr 20 Workshop, Warsaw, July 2013, Ian M. Anderson, Charles G. Torre
Gr 20 Workshop, Warsaw, July 2013, Ian M. Anderson, Charles G. Torre
Presentations
These are the Maple worksheets used at the Differential Geometry in Maple Workshop, which was held at the 20th International Conference on General Relativity and Gravitation, in Warsaw, July 2013.
There are 6 worksheets which can be downloaded from the list of files below.
Rainich-Type Conditions For Null Electrovacuum Spacetimes I, Charles G. Torre
Rainich-Type Conditions For Null Electrovacuum Spacetimes I, Charles G. Torre
Research Vignettes
In this worksheet I describe local Rainich-type conditions on a spacetime geometry which are necessary and sufficient for the existence of a solution of the Einstein-Maxwell equations with a null electromagnetic field. When it exists, the electromagnetic field is easily constructed.
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.