Physical Sciences and Mathematics Commons^™

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.

How Uncertainty In The Neutral Wind Limits The Accuracy Of Ionospheric Modeling And Forecasting, Michael David, Jan J. Sojka, Robert W. Schunk

Publications

One of the most important input fields for an ionospheric model is the horizontal neutral wind. The primary mechanism by which the neutral wind affects ionospheric densities is the inducement of an upward or downward ion drift along the magnetic field lines; this affects the rate at which ions are lost through recombination. The magnitude of this effect depends upon the dip angle of the magnetic field; for this reason, the impact of the neutral wind is somewhat less in polar regions than at mid-latitudes. It is unfortunate that observations of the neutral wind are relatively scarce, as compared for …

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.

Data From: How Uncertainty In The Neutral Wind Limits The Accuracy Of Ionospheric Modeling And Forecasting, Michael David, Jan Sojka, Robert W. Schunk

Browse all Datasets

Output files from runs of the TDIM ionospheric model used for the figures and calculations in the article in JGR Space Physics.

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)).

Geometrization Conditions For Perfect Fluids, Scalar Fields, And Electromagnetic Fields, Charles G. Torre, Dionisios Krongos

Charles G. Torre

Rainich-type 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 Einstein-scalar field equations and formulas for constructing the scalar field from …

The Riemann Curvature Tensor, Its Invariants, And Their Use In The Classification Of Spacetimes, Jesse Hicks

Presentations and Publications

The equivalence problem in general relativity is to determine whether two solutions of the Einstein field equations are isometric. Petrov has given a classification of metrics according to their isometry algebras. This talk discusses the use of the Petrov classification scheme, together with the use of scalar curvature invariants, to address the equivalence problem. These are the slides for a presentation at the Mathematics Association of America Spring 2015 conference at Brigham Young University.

Geometrization Conditions For Perfect Fluids, Scalar Fields, And Electromagnetic Fields, Charles G. Torre, Dionisios Krongos

Presentations and Publications

Rainich-type 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 Einstein-scalar field equations and for- mulas for constructing …

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.

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 …

Welcome And Opening Remarks, Rick C. Chappell

Magnetospheric-Ionospheric Coupling Conference

No abstract provided.

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 …

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 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 …

Annual Solar Motion And Spy Satellites, Margaret Jensen, Shane L. Larson

Browse All Undergraduate research

A topic often taught in introductory astronomy courses is the changing position of the Sun in the sky as a function of time of day, and season. The relevance and importance of this motion is explained in the context of seasons and the impact it has on human activities such as agriculture. The geometry of the ob- served motion in the sky is usually reduced to graphical representations and visualizations that can be difficult to render and grasp. Sometimes students are asked to observe the Suns changing motion and record their data, but this is a long-term project requiring several …

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 …

Understanding Light Pollution In And Around Tucson, Arizona, Rachel K. Nydegger

Browse All Undergraduate research

No abstract provided.

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.

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 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 …

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.

Quantifying Night Sky Fluctuations: Striving For A Multi-Messenger Astronomy, Rachel K. Nydegger, Shane L. Larson Ph.D.

Browse All Undergraduate research

With LIGO coming back online soon, astronomers are attempting to solve the problems involved with coupling gravitational observations with electromagnetic telescope observations. To do this, my project aims to create all-sky surveys to characterize natural variability to reduce "false-alarm" rates in detections of gravitational emissions.

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.

Prospects For Observing Ultracompact Binaries With Space-Based Gravitational Wave Interferometers And Optical Telescopes., T. B. Littenberg, Shane L. Larson, G. Nelemans Department Of Astrophysics, Radboud University Nijmegen, N. J. Cornish

All Physics Faculty Publications

Space-based gravitational wave interferometers are sensitive to the galactic population of ultra-compact binaries. An important subset of the ultra-compact binary popula- tion are those stars that can be individually resolved by both gravitational wave in- terferometers and electromagnetic telescopes. The aim of this paper is to quantify the multi-messenger potential of space-based interferometers with arm-lengths between 1 and 5 Gm. The Fisher Information Matrix is used to estimate the number of binaries from a model of the Milky Way which are localized on the sky by the gravitational wave detector to within 1 and 10 deg2 and bright enough to …

Characterizing Sky Variability For Multi-Messenger Astronomy, Rachel Nydegger

UCUR

Multi-messenger astronomy employs both electromagnetic and gravitational -wave detectors to paint a richer picture of celestial objects, providing more depth and information. The interferometers utilized for gravitational-wave observations receive input from very broad fields of view on the sky, typically a few square degrees. To have simultaneous electromagnetic observations (typically less than one square degree) requires innovative techniques for the telescopes to find the origin of radiation. One idea is to “tile” the view of the interferometer, using multiple telescopes to simultaneously point at different areas of the field to observe the source. One di"culty of this observing paradigm is …

Mapping Light Pollution At Utah State University, Rachel Nydegger, Shane L. Larson

Research on the Hill (Salt Lake City)

One of the beauties of modern civilization is seeing the city lighting at night. It provides a feeling of security and is indicative of the power and endeavors of humanity, but over-lighting is a form of pollution. Many outdoor light fixtures spread light in all directions, sending a majority of the light into the sky, away from where we want the light to be on the ground. This light spreading upward is not only wasted light, but it is wasted energy and money, destroys our ability to view the night sky, and has profound effects on nocturnal creatures. The direct …

Galaxy Inclination And Surface Brightness, Jordan C. Rozum, Shane L. Larson

Student Showcase

The distribution of spiral and bar galaxy inclination angles is expected to be uniform. However, analysis of several major galaxy catalogs shows this is not the case; galaxies oriented near edge-on are significantly more common in these catalogs. In an attempt to explain this discrepancy, we have developed a galaxy simulation code to compute the appearance of a spiral type galaxy as a function of its morphological parameters. We examine the dependence of observed brightness upon inclination angle by using smooth luminous mass density and interstellar medium (ISM) density distributions. The luminous mass component is integrated along a particular line …

Modeling Spiral Galaxy Luminosity Profiles, Jordan Rozum, Matt Garlock, Shane L. Larson, Bradley W. Carroll

Browse All Undergraduate research

The distribution of spiral and bar galaxy inclination an- gles is expected to be uniform. However, analysis of sev- eral major galaxy catalogs shows this is not the case; galaxies oriented near edge-on are significantly more common in these catalogs. In an attempt to explain this discrepancy, we have developed a galaxy simulation code to compute the appearance of a spiral type galaxy as a function of its morphological parameters. We examine the dependence of observed brightness upon inclination angle by using smooth luminous mass density and in- terstellar medium (ISM) density distributions. The lu- minous mass component is integrated …

Characterizing Sky Variability For Multi-Messenger Astronomy, Rachel Nydegger, Katie Breivik, Shane L. Larson

Browse All Undergraduate research

Multi-messenger astronomy employs both electromagnetic and gravitational wave detectors to paint a richer picture of celestial objects, providing more depth and in formation. Localizing sources with gravitational wave interferometers on the sky is difficult, with resolution of many square degrees. To have simultaneous electromagnetic observations (localized typically to less than one square degree) requires innovative techniques for the telescopes to find the origin of radiation. One idea is to tile the view of the interferometer, using multiple telescopes to simultaneously point at different areas of the field to observe the source. One problematic aspect of this observing paradigm is distinguishing …

Low Earth Orbiting Photographer (Leop) Cube Satellite, Jan J. Sojka, J. Alex Landon

Posters

The exploration and study of space is critical for the future of our society, but the opportunities for educational institutions to get involved in space research have faded dramatically in the last decade with the retirement of the space shuttle program. The USU Get Away Special (GAS) team is designing a new, low cost solution to space research, CubeSat (Cube Satellite). This small satellite, with a volume of approximately one liter, will have a high resolution camera directed at earth, and students will be able to request a picture of their area when the satellite flies overhead. In this way, …

From The Big Bang To The Swaner Ecocenter: The Cosmic Biography Of Atoms, Shane L. Larson

Public Talks

No abstract provided.

Probing The Cosmos With Light And Gravity: Multi-Messenger Astronomy In The Gravitational Wave Era, Shane L. Larson

Colloquia and Seminars

No abstract provided.