Physical Sciences and Mathematics Commons^™

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

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.

Installation instructions

A New Non-Inheriting Homogeneous Solution Of The Einstein-Maxwell Equations With Cosmological Term, Ian M. Anderson, Charles G. Torre

Publications

We find a new homogeneous solution to the Einstein-Maxwell equations with a cos- mological term. The spacetime manifold is R × S3. The spacetime metric admits a simply transitive isometry group G = R × SU(2) and is Petrov type I. The spacetime is geodesically complete and globally hyperbolic. The electromagnetic field is non- null and non-inheriting: it is only invariant with respect to the SU(2) subgroup and is time-dependent in a stationary reference frame.

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.

Standard Non-Uniform Noise Dataset, Andres Imperial, John M. Edwards

Browse all Datasets

Fixed Pattern Noise Non-Uniformity Correction through K-Means Clustering

Fixed pattern noise removal from imagery by software correction is a practical approach compared to a physical hardware correction because it allows for correction post-capture of the imagery. Fixed pattern noise presents a unique challenge for de-noising techniques as the noise does not present itself where large number statistics are effective. Traditional noise removal techniques such as blurring or despeckling produce poor correction results because of a lack of noise identification. Other correction methods developed for fixed pattern noise can often present another problem of misidentification of noise. This problem can result …

Radiometric Stability Of The Saber Instrument, Martin G. Mlynczak, Taumi Daniels, Linda A. Hunt, Jia Yue, B. Thomas Marshall, James M. Russell Iii, Ellis E. Remsburg, Joseph Tansock, Roy Esplin, Mark Jensen, Andrew Shumway, Larry Gordley, J. -H. Yee

Space Dynamics Laboratory Publications

The SABER instrument on the National Aeronautics and Space Administration Thermosphere‐Ionosphere‐Mesosphere Energetics and Dynamics satellite continues to provide a long‐term record of Earth's stratosphere, mesosphere, and lower thermosphere. The SABER data are being used to examine long‐term changes and trends in temperature, water vapor, and carbon dioxide. A tacit, central assumption of these analyses is that the SABER instrument radiometric calibration is not changing with time; that is, the instrument is stable. SABER stratospheric temperatures and those derived from Global Positioning System Radio Occultation measurements are compared to examine SABER's stability. Global Positioning System Radio Occultation measurements are inherently stable …

Meps Data Assimilation System, Robert W. Schunk, Larry Gardner

Browse all Datasets

For the current funding opportunity we propose to develop a master system that will enhance the user interface to the MEPS model and enable the scientific community to efficiently use the model. Furthermore, we will build and automate validation tools and improve the efficiency and robustness of the MEPS ensemble averaging scheme. Finally, we will explore the nest step toward a major advancement in MEPS b significantly improving the spatial resolution of one of the data assimilation models to explore meso- and small-scale features.

Simultaneous In Situ Measurements Of Small-Scale Structures In Neutral, Plasma, And Atomic Oxygen Densities During The Wadis Sounding Rocket Project, Boris Strelnikov, Martin Eberhart, Martin Friedrich, Jonas Hedin, Mikhail Khaplanov, Gerd Baumgarten, Bifford P. Williams, Tristan Staszak, Heiner Asmus, Irina Strelnikova, Ralph Latteck, Mykhaylo Grygalashvyly, Franz-Josef Lübken, Josef Höffner, Raimund Wörl, Jörg Gumbel, Stefan Löhle, Stefanos Fasoulas, Markus Rapp, Aroh Barjatya, Michael J. Taylor, Pierre-Dominique Pautet

Publications

In this paper we present an overview of measurements conducted during the WADIS-2 rocket campaign. We investigate the effect of small-scale processes like gravity waves and turbulence on the distribution of atomic oxygen and other species in the mesosphere–lower thermosphere (MLT) region. Our analysis suggests that density fluctuations of atomic oxygen are coupled to fluctuations of other constituents, i.e., plasma and neutrals. Our measurements show that all measured quantities, including winds, densities, and temperatures, reveal signatures of both waves and turbulence. We show observations of gravity wave saturation and breakdown together with simultaneous measurements of generated turbulence. Atomic oxygen inside …

A Near Horizon Extreme Binary Black Hole Geometry, Jacob Ciafre, Maria J. Rodriguez

All Physics Faculty Presentations

A new solution of four-dimensional vacuum General Relativity is presented. It describes the near horizon region of the extreme (maximally spinning) binary black hole system with two identical extreme Kerr black holes held in equilibrium by a massless strut. This is the first example of a non-supersymmetric, near horizon extreme binary black hole geometry of two uncharged black holes. The black holes are co-rotating, their relative distance is fixed, and the solution is uniquely specified by the mass. Asymptotically, the geometry corresponds to the near horizon extreme Kerr (NHEK) black hole. The binary extreme system has finite entropy.

Large‐Amplitude Mountain Waves In The Mesosphere Observed On 21 June 2014 During Deepwave: 1.Wave Development, Scales, Momentum Fluxes, And Environmental Sensitivity, Michael J. Taylor, Pierre-Dominique Pautet, David C. Fritts, Bernd Kaifler, Steven M. Smith, Yucheng Zhao, Neal R. Criddle, Pattilyn Mclaughlin, William R. Pendleton Jr., Michael P. Mccarthy, Gonzalo Hernandez, Stephen D. Eckermann, James Doyle, Markus Rapp, Ben Liley, James M. Russell Iii

Publications

A remarkable, large‐amplitude, mountain wave (MW) breaking event was observed on the night of 21 June 2014 by ground‐based optical instruments operated on the New Zealand South Island during the Deep Propagating Gravity Wave Experiment (DEEPWAVE). Concurrent measurements of the MW structures, amplitudes, and background environment were made using an Advanced Mesospheric Temperature Mapper, a Rayleigh Lidar, an All‐Sky Imager, and a Fabry‐Perot Interferometer. The MW event was observed primarily in the OH airglow emission layer at an altitude of ~82 km, over an ~2‐hr interval (~10:30–12:30 UT), during strong eastward winds at the OH altitude and above, which weakened …

"Collaborative Research: Cedar--Airglow Imaging Of Gravity Wave And Instability Dynamics,", Michael Taylor

Funded Research Records

No abstract provided.

Regional Distribution Of Mesospheric Small‐Scale Gravity Waves During Deepwave, Pierre-Dominique Pautet, Michael J. Taylor, S. D. Eckermann, Neal R. Criddle

Publications

The Deep Propagating Gravity Wave Experiment project took place in June and July 2014 in New Zealand. Its overarching goal was to study gravity waves (GWs) as they propagate from the ground up to ~100 km, with a large number of ground‐based, airborne, and satellite instruments, combined with numerical forecast models. A suite of three mesospheric airglow imagers operated onboard the NSF Gulfstream V (GV) aircraft during 25 nighttime flights, recording the GW activity at OH altitude over a large region (>7,000,000 km²). Analysis of this data set reveals the distribution of the small‐scale GW mean power …

On The Balance Between Plasma And Magnetic Pressure Across Equatorial Plasma Depletions, J. Rodríguez-Zuluaga, C. Stolle, Y. Yamazaki, H. Lühr, J. Park, Ludger Scherliess, J. L. Chau

All Physics Faculty Publications

In magnetized plasmas such as the ionosphere, electric currents develop in regions of strong density gradients to balance the resulting plasma pressure gradients. These currents, usually known as diamagnetic currents decrease the magnetic pressure where the plasma pressure increases, and vice versa. In the low‐latitude ionosphere, equatorial plasma depletions (EPDs) are well known for their steep plasma density gradients and adverse effect on radio wave propagation. In this paper, we use continuous measurements of the magnetic field and electron density from the European Space Agency's Swarm constellation mission to assess the balance between plasma and magnetic pressure across large‐scale EPDs. …

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 …

Does The Black Hole Shadow Probe The Event Horizon Geometry?, Pedro V. P. Cunha, Carlos A. R. Herdeiro, Maria J. Rodriguez

All Physics Faculty Publications

There is an exciting prospect of obtaining the shadow of astrophysical black holes (BHs) in the near future with the Event Horizon Telescope. As a matter of principle, this justifies asking how much one can learn about the BH horizon itself from such a measurement. Since the shadow is determined by a set of special photon orbits, rather than horizon properties, it is possible that different horizon geometries yield similar shadows. One may then ask how sensitive is the shadow to details of the horizon geometry? As a case study, we consider the double Schwarzschild BH and analyze the impact …

Data From: Polar Topside Ionosphere During Geomagnetic Storms: Comparison Of Isis-Ii With Tdim, Jan J. Sojka, Dan Rice, Michael David, Robert W. Schunk, Robert Benson, H. G. James

Browse all Datasets

Output files from runs of the TDIM ionospheric model used for calculations and electron density profiles from ISIS-II and TDIM used in figures in the article in Radio Science.

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

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

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.

Investigating The Opal Cubesat’S Ability To Measure Thermospheric Gravity Waves, Kenneth Zia, Michael J. Taylor, Ludger Scherliess

Posters

Understanding the Earth’s lower thermosphere is of high interest to the space science community because of competing forcing due to solar heating above and episodic wave forcing from below. The NSF sponsored OPAL cubesat is designed to measure the temperature profile in this region by observing day-time O2 A time O2 A-band (~760nm) emission on the limb and is expected to be launched from the ISS (International Space Station). To band (~760nm) emission on the limb and is expected to be launched from the ISS (International Space Station). To investigate the instrument’s ability to detect space weather signatures (i.e. solar …

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.

How Hospitable Are Space Weather Affected Habitable Zones? The Role Of Ion Escape, Vladimir S. Airapetian, Alex Glocer, George V. Khazanov, Robert O Parke Loyd, Kevin France, Jan Josef Sojka, William C. Danchi, Michael W. Liemohn

All Physics Faculty Publications

Atmospheres of exoplanets in the habitable zones around active young G-K-M stars are subject to extreme X-ray and EUV (XUV) fluxes from their host stars that can initiate atmospheric erosion. Atmospheric loss affects exoplanetary habitability in terms of surface water inventory, atmospheric pressure, the efficiency of greenhouse warming, and the dosage of the UV surface irradiation. Thermal escape models suggest that exoplanetary atmospheres around active K-M stars should undergo massive hydrogen escape, while heavier species including oxygen will accumulate forming an oxidizing atmosphere. Here, we show that non-thermal oxygen ion escape could be as important as thermal, hydrodynamic H escape …

Climatology Of Plasmaspheric Total Electron Content Obtained From Jason 1 Satellite, Ja Soon Shim, Geonhwa Jee, Ludger Scherliess

All Physics Faculty Publications

We used more than 40 million total electron content (TEC) measurements obtained from the GPS TurboRogue Space Receiver receiver on board the Jason 1 satellite in order to investigate the global morphology of the plasmaspheric TEC (pTEC) including the variations with local time, latitude, longitude, season, solar cycle, and geomagnetic activity. The pTEC corresponds to the total electron content between Jason 1 (1336 km) and GPS (20,200 km) satellite altitudes. The pTEC data were collected during the 7 year period from January 2002 to December 2008. It was found that pTEC increases by about 10–30% from low to high solar …

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)).

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 …