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FullText Articles in Physics
Introduction To Classical Field Theory, Charles G. Torre
Introduction To Classical Field Theory, Charles G. Torre
All Complete Monographs
This is an introduction to classical field theory. Topics treated include: KleinGordon field, electromagnetic field, scalar electrodynamics, Dirac field, YangMills field, gravitational field, Noether theorems relating symmetries and conservation laws, spontaneous symmetry breaking, Lagrangian and Hamiltonian formalisms.
Gravity Waves Over Antarctica, Vanessa Chambers
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
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
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
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.
Geometrization Conditions For Perfect Fluids, Scalar Fields, And Electromagnetic Fields, Charles G. Torre, Dionisios Krongos
Geometrization Conditions For Perfect Fluids, Scalar Fields, And Electromagnetic Fields, Charles G. Torre, Dionisios Krongos
Charles G. Torre
Rainichtype 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 Einsteinscalar 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
Geometrization Conditions For Perfect Fluids, Scalar Fields, And Electromagnetic Fields, Charles G. Torre, Dionisios Krongos
Presentations and Publications
Rainichtype 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 Einsteinscalar field equations and for mulas for constructing ...
RainichType Conditions For Perfect Fluid Spacetimes, Dionisios Krongos, Charles G. Torre
RainichType 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 Rainichtype conditions on an ndimensional 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 Rainichtype 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
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
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 EinsteinMaxwell 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 nonnull electrovacua. Given a spacetime satisfying the conditions for a null electrovacuum, a straightforward procedure builds the null electromagnetic field from ...
RainichType Conditions For Null Electrovacuum Spacetimes Ii, Charles G. Torre
RainichType Conditions For Null Electrovacuum Spacetimes Ii, Charles G. Torre
Research Vignettes
In this second of two worksheets I continue describing local Rainichtype 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 EinsteinMaxwell 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
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 EinsteinMaxwell 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 nonnull 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
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
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 highredshift population of intermediatemass black holes (IMBHs), with masses M_{•} in the range 10^{2}≲M_{•}≲ 10^{5} 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 GravitationalWave Background: The Overlap Reduction Function, Lee Samuel Finn, Shane L. Larson, Joseph D. Romano
Detecting A Stochastic GravitationalWave Background: The Overlap Reduction Function, Lee Samuel Finn, Shane L. Larson, Joseph D. Romano
All Physics Faculty Publications
Detection of a gravitationalwave stochastic background via ground or spacebased gravitationalwave detectors requires the cross correlation of the response of two or more independent detectors. The cross correlation involves a frequencydependent factor—the socalled overlap reduction function or HellingsDowns 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 gravitationalwave 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
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 × 10^{6} 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, HolleyBockelmann & Finn (2006). Here we give an analytical estimate of the ...
SemiRelativistic Approximation To Gravitational Radiation From Encounters With NonSpinning Black Holes, Jonathan R. Gair, Daniel J. Kennefick, Shane L. Larson
SemiRelativistic Approximation To Gravitational Radiation From Encounters With NonSpinning 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 TimeDelay Interferometry ZeroSignal Solution: Geometrical Properties, Massimo Tinto, Shane L. Larson
Lisa TimeDelay Interferometry ZeroSignal Solution: Geometrical Properties, Massimo Tinto, Shane L. Larson
All Physics Faculty Publications
Timedelay 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 zerosignal solution (ZSS). This is a twoparameter 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
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 AMFM 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
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 m_{g} by comparing the arrival times of gravitational and electromagnetic signals from binary star systems. We show that the best possible limit on m_{g} obtainable this way is ∼50 times better than the current limit set by solar system measurements. Among currently known, wellunderstood binaries, 4U182030 is the best for this purpose; LISA observations of 4U182030 should yield a limit ≈34 times better than the present solar system bound. AM ...
Unequal Arm SpaceBorne Gravitational Wave Detectors, Shane L. Larson, Ronald W. Hellings, William A. Hiscock
Unequal Arm SpaceBorne Gravitational Wave Detectors, Shane L. Larson, Ronald W. Hellings, William A. Hiscock
All Physics Faculty Publications
Unlike groundbased interferometric gravitational wave detectors, large spacebased 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
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
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 spacebased 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
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
Semiclassical Effects In Black Hole Interiors, William A. Hiscock, Shane L. Larson, Paul R. Anderson
All Physics Faculty Publications
Firstorder 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 stressenergy of quantized scalar, spinor, and vector fields, evaluated using analytic approximations developed by Page and others (for massless fields) and the DeWittSchwinger 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 ...