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Full-Text Articles in Physics

Introduction To Classical Field Theory, Charles G. Torre Aug 2019

Introduction To Classical Field Theory, Charles G. Torre

All Complete Monographs

This is an introduction to classical field theory. Topics treated include: Klein-Gordon field, electromagnetic field, scalar electrodynamics, Dirac field, Yang-Mills field, gravitational field, Noether theorems relating symmetries and conservation laws, spontaneous symmetry breaking, Lagrangian and Hamiltonian formalisms.


Gravity Waves Over Antarctica, Vanessa Chambers May 2018

Gravity Waves Over Antarctica, Vanessa Chambers

Physics Capstone Project

As part of the international Antarctic Gravity Wave Instrument Network (ANGWIN) program, the Utah State University all sky IR imager has been operated at the British Antarctic Survey (BAS) Halley Station (75°36′ S, 26°12′ W) since 2012, obtaining valuable gravity wave information in the upper mesosphere and lower thermosphere region (~80 to 100 km). In this study, we have utilized a new 3D spectral analysis technique (Matsuda, et al., 2014) to quantify the horizontal phase velocity distributions of gravity waves over Antarctica. This new tool enables us to analyze extensive amounts of airglow imaging data in a relatively ...


Does The Black Hole Shadow Probe The Event Horizon Geometry?, Pedro V. P. Cunha, Carlos A. R. Herdeiro, Maria J. Rodriguez Apr 2018

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 ...


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


Geometrization Conditions For Perfect Fluids, Scalar Fields, And Electromagnetic Fields, Charles G. Torre, Dionisios Krongos Jul 2015

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 ...


Geometrization Conditions For Perfect Fluids, Scalar Fields, And Electromagnetic Fields, Charles G. Torre, Dionisios Krongos Mar 2015

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 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.


Perihelion Precession In General Relativity, Charles G. Torre Apr 2014

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 Feb 2014

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 ...


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 ...


The Spacetime Geometry Of A Null Electromagnetic Field, Charles G. Torre Jul 2013

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 ...


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.


Constraining The Black Hole Mass Spectrum With Gravitational Wave Observations – I. The Error Kernel, Danny C. Jacobs, Joseph E. Plowman, Ronald W. Hellings, Sachiko Tsuruta, Shane L. Larson Feb 2010

Constraining The Black Hole Mass Spectrum With Gravitational Wave Observations – I. The Error Kernel, Danny C. Jacobs, Joseph E. Plowman, Ronald W. Hellings, Sachiko Tsuruta, Shane L. Larson

All Physics Faculty Publications

Many scenarios have been proposed for the origin of the supermassive black holes (SMBHs) that are found in the centres of most galaxies. Many of these formation scenarios predict a high-redshift population of intermediate-mass black holes (IMBHs), with masses M in the range 102M≲ 105 M. A powerful way to observe these IMBHs is via gravitational waves the black holes emit as they merge. The statistics of the observed black hole population should, in principle, allow us to discriminate between competing astrophysical scenarios for the origin and formation of SMBHs. However, gravitational wave detectors such as Laser ...


Detecting A Stochastic Gravitational-Wave Background: The Overlap Reduction Function, Lee Samuel Finn, Shane L. Larson, Joseph D. Romano Jan 2009

Detecting A Stochastic Gravitational-Wave Background: The Overlap Reduction Function, Lee Samuel Finn, Shane L. Larson, Joseph D. Romano

All Physics Faculty Publications

Detection of a gravitational-wave stochastic background via ground or space-based gravitational-wave detectors requires the cross correlation of the response of two or more independent detectors. The cross correlation involves a frequency-dependent factor—the so-called overlap reduction function or Hellings-Downs curve—that depends on the relative geometry of each detector pair, i.e., the detector separations and the relative orientation of their antenna patterns (beams). An incorrect formulation of this geometrical factor has appeared in the literature, leading to incorrect conclusions regarding the sensitivity of proposed detectors to a stochastic gravitational-wave background. To rectify these errors and as a reference for ...


Gravitational Wave Bursts From The Galactic Massive Black Hole, Clovis Hopman, Marc Freitag, Shane L. Larson Jun 2007

Gravitational Wave Bursts From The Galactic Massive Black Hole, Clovis Hopman, Marc Freitag, Shane L. Larson

All Physics Faculty Publications

The Galactic massive black hole (MBH), with a mass of M= 3.6 × 106 M, is the closest known MBH, at a distance of only 8 kpc. The proximity of this MBH makes it possible to observe gravitational waves (GWs) from stars with periapse in the observational frequency window of the Laser Interferometer Space Antenna (LISA). This is possible even if the orbit of the star is very eccentric, so that the orbital frequency is many orders of magnitude below the LISA frequency window, as suggested by Rubbo, Holley-Bockelmann & Finn (2006). Here we give an analytical estimate of the ...


Semi-Relativistic Approximation To Gravitational Radiation From Encounters With Non-Spinning Black Holes, Jonathan R. Gair, Daniel J. Kennefick, Shane L. Larson Jan 2005

Semi-Relativistic Approximation To Gravitational Radiation From Encounters With Non-Spinning Black Holes, Jonathan R. Gair, Daniel J. Kennefick, Shane L. Larson

All Physics Faculty Publications

The capture of compact bodies by black holes in galactic nuclei is an important prospective source for low frequency gravitational wave detectors, such as the planned Laser Interferometer Space Antenna. This paper calculates, using a semirelativistic approximation, the total energy and angular momentum lost to gravitational radiation by compact bodies on very high eccentricity orbits passing close to a supermassive, nonspinning black hole; these quantities determine the characteristics of the orbital evolution necessary to estimate the capture rate. The semirelativistic approximation improves upon treatments which use orbits at Newtonian order and quadrupolar radiation emission, and matches well onto accurate Teukolsky ...


Lisa Time-Delay Interferometry Zero-Signal Solution: Geometrical Properties, Massimo Tinto, Shane L. Larson Jan 2004

Lisa Time-Delay Interferometry Zero-Signal Solution: Geometrical Properties, Massimo Tinto, Shane L. Larson

All Physics Faculty Publications

Time-delay interferometry (TDI) is the data processing technique needed for generating interferometric combinations of data measured by the multiple Doppler readouts available onboard the three Laser Interferometer Space Antenna (LISA) spacecraft. Within the space of all possible interferometric combinations TDI can generate, we have derived a specific combination that has zero response to the gravitational wave signal, and called it the zero-signal solution (ZSS). This is a two-parameter family of linear combinations of the generators of the TDI space, and its response to a gravitational wave becomes null when these two parameters coincide with the values of the angles of ...


Lisa Data Analysis: Source Identification And Subtraction, Neil J. Cornish, Shane L. Larson Jan 2003

Lisa Data Analysis: Source Identification And Subtraction, Neil J. Cornish, Shane L. Larson

All Physics Faculty Publications

The Laser Interferometer Space Antenna will operate as an AM-FM receiver for gravitational waves. For binary systems, the source location, orientation and orbital phase are encoded in the amplitude and frequency modulation. The same modulations spread a monochromatic signal over a range of frequencies, making it difficult to identify individual sources. We present a method for detecting and subtracting individual binary signals from a data stream with many overlapping signals.


Lisa, Binary Stars, And The Mass Of The Graviton, Curt Cutler, William A. Hiscock, Shane L. Larson Jan 2003

Lisa, Binary Stars, And The Mass Of The Graviton, Curt Cutler, William A. Hiscock, Shane L. Larson

All Physics Faculty Publications

We extend and improve earlier estimates of the ability of the proposed LISA (Laser Interferometer Space Antenna) gravitational wave detector to place upper bounds on the graviton mass mg by comparing the arrival times of gravitational and electromagnetic signals from binary star systems. We show that the best possible limit on mg obtainable this way is ∼50 times better than the current limit set by solar system measurements. Among currently known, well-understood binaries, 4U1820-30 is the best for this purpose; LISA observations of 4U1820-30 should yield a limit ≈3-4 times better than the present solar system bound. AM ...


Unequal Arm Space-Borne Gravitational Wave Detectors, Shane L. Larson, Ronald W. Hellings, William A. Hiscock Jan 2002

Unequal Arm Space-Borne Gravitational Wave Detectors, Shane L. Larson, Ronald W. Hellings, William A. Hiscock

All Physics Faculty Publications

Unlike ground-based interferometric gravitational wave detectors, large space-based systems will not be rigid structures. When the end stations of the laser interferometer are freely flying spacecraft, the armlengths will change due to variations in the spacecraft positions along their orbital trajectories, so the precise equality of the arms that is required in a laboratory interferometer to cancel laser phase noise is not possible. However, using a method discovered by Tinto and Armstrong, a signal can be constructed in which laser phase noise exactly cancels out, even in an unequal arm interferometer. We examine the case where the ratio of the ...


Sensitivity Curves For Spaceborne Gravitational Wave Interferometers, Shane L. Larson, William A. Hiscock, Ronald W. Hellings Jan 2000

Sensitivity Curves For Spaceborne Gravitational Wave Interferometers, Shane L. Larson, William A. Hiscock, Ronald W. Hellings

All Physics Faculty Publications

To determine whether particular sources of gravitational radiation will be detectable by a specific gravitational wave detector, it is necessary to know the sensitivity limits of the instrument. These instrumental sensitivities are often depicted (after averaging over source position and polarization) by graphing the minimal values of the gravitational wave amplitude detectable by the instrument versus the frequency of the gravitational wave. This paper describes in detail how to compute such a sensitivity curve given a set of specifications for a spaceborne laser interferometer gravitational wave observatory. Minor errors in the prior literature are corrected, and the first (mostly) analytic ...


Using Binary Star Observations To Bound The Mass Of The Graviton, Shane L. Larson, William A. Hiscock Jan 2000

Using Binary Star Observations To Bound The Mass Of The Graviton, Shane L. Larson, William A. Hiscock

All Physics Faculty Publications

Interacting white dwarf binary star systems, including helium cataclysmic variable (HeCV) systems, are expected to be strong sources of gravitational radiation, and should be detectable by proposed space-based laser interferometer gravitational wave observatories such as LISA. Several HeCV star systems are presently known and can be studied optically, which will allow electromagnetic and gravitational wave observations to be correlated. Comparisons of the phases of a gravitational wave signal and the orbital light curve from an interacting binary white dwarf star system can be used to bound the mass of the graviton. Observations of typical HeCV systems by LISA could potentially ...


Astrophysical Bounds On Global Strings, Shane L. Larson, William A. Hiscock Jan 1997

Astrophysical Bounds On Global Strings, Shane L. Larson, William A. Hiscock

All Physics Faculty Publications

Global topological defects produce nonzero stress energy throughout spacetime, and as a result can have observable gravitational influence on surrounding matter. Gravitational effects of global strings are used to place bounds on their cosmic abundance. The minimum separation between global strings is estimated by considering the defects' contribution to the cosmological energy density. More rigorous constraints on the abundance of global strings are constructed by examining the tidal forces such defects will have on observable astrophysical systems. The small number of observed tidally disrupted systems indicates there can be very few of these objects in the observable Universe.


Semiclassical Effects In Black Hole Interiors, William A. Hiscock, Shane L. Larson, Paul R. Anderson Jan 1997

Semiclassical Effects In Black Hole Interiors, William A. Hiscock, Shane L. Larson, Paul R. Anderson

All Physics Faculty Publications

First-order semiclassical perturbations to the Schwarzschild black hole geometry are studied within the black hole interior. The source of the perturbations is taken to be the vacuum stress-energy of quantized scalar, spinor, and vector fields, evaluated using analytic approximations developed by Page and others (for massless fields) and the DeWitt-Schwinger approximation (for massive fields). Viewing the interior as an anisotropic collapsing cosmology, we find that minimally or conformally coupled scalar fields, and spinor fields, decrease the anisotropy as the singularity is approached, while vector fields increase the anisotropy. In addition, we find that for massless fields of all spins, the ...