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2012

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Articles 1 - 30 of 34

Full-Text Articles in Cosmology, Relativity, and Gravity

Molecular Processes In Astrophysics: Calculations Of H + H2 Excitation, De-Excitation, And Cooling, Matthew Kelley Dec 2012

Molecular Processes In Astrophysics: Calculations Of H + H2 Excitation, De-Excitation, And Cooling, Matthew Kelley

UNLV Theses, Dissertations, Professional Papers, and Capstones

The implications of H+H2 cooling in astrophysics is important to several applications. One of the most significant and pure applications is its role in cooling in the early universe. Other applications would include molecular dynamics in nebulae and their collapse into stars and astrophysical shocks. Shortly after the big bang, the universe was a hot primordial gas of photons, electrons, and nuclei among other ingredients. By far the most dominant nuclei in the early universe was hydrogen. In fact, in the early universe the matter density was 90 percent hydrogen and only 10 percent helium with small amounts of lithium …


Topics In Galaxy Formation: Pairwise Velocities Of Dark Matter Halos And Molecular Hydrogen Regulated Star Formation In Cosmological Simulations, Robert Jo Thompson Dec 2012

Topics In Galaxy Formation: Pairwise Velocities Of Dark Matter Halos And Molecular Hydrogen Regulated Star Formation In Cosmological Simulations, Robert Jo Thompson

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this dissertation we investigate two distinct challenges within the concordance LCDM model and an unrelated project.

The first is a discrepancy between theory and observation. A massive galaxy sub-cluster known as the `bullet' has fallen through a more massive parent galaxy cluster at a redshift of z=0.296.

Theory finds that in order to reproduce the observational quantities of this cluster, an unusually high relative velocity of v12=3000 km/s between the two cluster's parent halos is required.

We quantify the statistical probability of producing a `bullet-like' halo pair within large N-body simulations, and

conclude that either the LCDM model is …


On The Spherical Symmetry Of Perfect-Fluid Stellar Models In General Relativity, Joshua M Brewer Dec 2012

On The Spherical Symmetry Of Perfect-Fluid Stellar Models In General Relativity, Joshua M Brewer

Masters Theses

It is well known in Newtonian theory that static self-gravitating perfect fluids in a vacuum are necessarily spherically symmetric. The necessity of spherical symmetry of perfect-fluid static spacetimes with constant density in general relativity is shown.


The Disk-Wind-Jet Connection In The Black Hole H 1743-322, J. M. Miller, J. Raymond, A. C. Fabian, C. S. Reynolds, A. L. King, T. R. Kallman, E. M. Cackett, M. Van Der Klis, D. T. H. Steeghs Nov 2012

The Disk-Wind-Jet Connection In The Black Hole H 1743-322, J. M. Miller, J. Raymond, A. C. Fabian, C. S. Reynolds, A. L. King, T. R. Kallman, E. M. Cackett, M. Van Der Klis, D. T. H. Steeghs

Physics and Astronomy Faculty Research Publications

X-ray disk winds are detected in spectrally soft, disk-dominated phases of stellar-mass black hole outbursts. In contrast, compact, steady, relativistic jets are detected in spectrally hard states that are dominated by non-thermal X-ray emission. Although these distinctive outflows appear to be almost mutually exclusive, it is possible that a disk wind persists in hard states but cannot be detected via X-ray absorption lines owing to very high ionization. Here, we present an analysis of a deep, 60 ks Chandra/HETGS observation of the black hole candidate H 1743-322 in the low/hard state. The spectrum shows no evidence of a disk wind, …


Black Holes In The Conical Ensemble, Robert A. Mcnees Iv, Daniel Grumiller Oct 2012

Black Holes In The Conical Ensemble, Robert A. Mcnees Iv, Daniel Grumiller

Physics: Faculty Publications and Other Works

We consider black holes in an “unsuitable box”: a finite cavity coupled to a thermal reservoir at a temperature different than the black hole’s Hawking temperature. These black holes are described by metrics that are continuous but not differentiable due to a conical singularity at the horizon. We include them in the Euclidean path integral sum over configurations, and analyze the effect this has on black hole thermodynamics in the canonical ensemble. Black holes with a small deficit (or surplus) angle may have a smaller internal energy or larger density of states than the nearby smooth black hole, but they …


Cyclic Universe With An Inflationary Phase From A Cosmological Model With Real Gas Quintessence, Rossen Ivanov, Emil Prodanov Oct 2012

Cyclic Universe With An Inflationary Phase From A Cosmological Model With Real Gas Quintessence, Rossen Ivanov, Emil Prodanov

Articles

Phase-plane stability analysis of a dynamical system describing the Universe as a two-fraction uid containing baryonic dust and real virial gas quintessence is presented. Existence of a stable periodic solution experiencing in ationary periods is shown. A van der Waals quintessence model is revisited and cyclic Universe solution again found.


A Four-Year Xmm-Newton/Chandra Monitoring Campaign Of The Galactic Centre: Analysing The X-Ray Transients, N. Degenaar, R. Wijnands, E. M. Cackett, J. Homan, J. J. M. In 'T Zand, E. Kuulkers, T. J. Maccarone, M. Van Der Klis Sep 2012

A Four-Year Xmm-Newton/Chandra Monitoring Campaign Of The Galactic Centre: Analysing The X-Ray Transients, N. Degenaar, R. Wijnands, E. M. Cackett, J. Homan, J. J. M. In 'T Zand, E. Kuulkers, T. J. Maccarone, M. Van Der Klis

Physics and Astronomy Faculty Research Publications

We report on the results of a four-year long X-ray monitoring campaign of the central 1.2 square degrees of our Galaxy, performed with Chandra and XMM-Newton between 2005 and 2008. Our study focuses on the properties of transient X-ray sources that reach 2-10 keV luminosities of LX ≳ 1034 erg s-1 for an assumed distance of 8 kpc. There are 17 known X-ray transients within the field of view of our campaign, eight of which were detected in outburst during our observations: the transient neutron star low-mass X-ray binaries GRS 1741-2853, AX J1745.6-2901, SAX J1747.0-2853, KS 1741-293 …


On The Role Of The Accretion Disk In Black Hole Disk-Jet Connections, J. M. Miller, G. G. Pooley, A. C. Fabian, M. A. Nowak, R. C. Reis, E. M. Cackett, K. Pottschmidt, J. Wilms Sep 2012

On The Role Of The Accretion Disk In Black Hole Disk-Jet Connections, J. M. Miller, G. G. Pooley, A. C. Fabian, M. A. Nowak, R. C. Reis, E. M. Cackett, K. Pottschmidt, J. Wilms

Physics and Astronomy Faculty Research Publications

Models of jet production in black hole systems suggest that the properties of the accretion disk—such as its mass accretion rate, inner radius, and emergent magnetic field—should drive and modulate the production of relativistic jets. Stellar-mass black holes in the "low/hard" state are an excellent laboratory in which to study disk-jet connections, but few coordinated observations are made using spectrometers that can incisively probe the inner disk. We report on a series of 20 Suzaku observations of Cygnus X-1 made in the jet-producing low/hard state. Contemporaneous radio monitoring was done using the Arcminute MicroKelvin Array radio telescope. Two important and …


The Implementation Of The Shear Correlation Function And The Matter Power Spectrum In R, Allison A. Scheppelmann, Deborah J. Bard Aug 2012

The Implementation Of The Shear Correlation Function And The Matter Power Spectrum In R, Allison A. Scheppelmann, Deborah J. Bard

STAR Program Research Presentations

Weak gravitational lensing is an important tool in understanding the large-scale structure of the universe. One component in understanding the effect of weak gravitational lensing is the shear correlation function and matter power spectrum. The calculation of these values is often complicated and time consuming. In order to decrease the cost of these calculations they were implemented in R using parallelization. This resulted in the calculations completing faster and the process to be easily changed in order to fit the need of each researcher using the algorithms created in R.


A Comparison Of Broad Iron Emission Lines In Archival Data Of Neutron Star Low-Mass X-Ray Binaries, Edward M. Cackett, Jon M. Miller, Rubens C. Reis, Andrew C. Fabian, Didier Barret Aug 2012

A Comparison Of Broad Iron Emission Lines In Archival Data Of Neutron Star Low-Mass X-Ray Binaries, Edward M. Cackett, Jon M. Miller, Rubens C. Reis, Andrew C. Fabian, Didier Barret

Physics and Astronomy Faculty Research Publications

Relativistic X-ray disklines have been found in multiple neutron star low-mass X-ray binaries, in close analogy with black holes across the mass scale. These lines have tremendous diagnostic power and have been used to constrain stellar radii and magnetic fields, often finding values that are consistent with independent timing techniques. Here, we compare CCD-based data from Suzaku with Fe K line profiles from archival data taken with gas-based spectrometers. In general, we find good consistency between the gas-based line profiles from EXOSAT, BeppoSAX, and RXTE and the CCD data from Suzaku, demonstrating that the broad profiles seen are intrinsic to …


Information Content Of Spontaneous Symmetry Breaking, Marcelo Gleiser, Nikitas Stamatopoulos Aug 2012

Information Content Of Spontaneous Symmetry Breaking, Marcelo Gleiser, Nikitas Stamatopoulos

Dartmouth Scholarship

We propose a measure of order in the context of nonequilibrium field theory and argue that this measure, which we call relative configurational entropy (RCE), may be used to quantify the emergence of coherent low-entropy configurations, such as time-dependent or time-independent topological and nontopological spatially extended structures. As an illustration, we investigate the nonequilibrium dynamics of spontaneous symmetry breaking in three spatial dimensions. In particular, we focus on a model where a real scalar field, prepared initially in a symmetric thermal state, is quenched to a broken-symmetric state. For a certain range of initial temperatures, spatially localized, long-lived structures known …


Entropic Measure For Localized Energy Configurations: Kinks, Bounces, And Bubbles, Marcelo Gleiser, Nikitas Stamatopoulos Jul 2012

Entropic Measure For Localized Energy Configurations: Kinks, Bounces, And Bubbles, Marcelo Gleiser, Nikitas Stamatopoulos

Dartmouth Scholarship

No abstract provided.


On The Determination Of The Spin Of The Black Hole In Cyg X-1 From X-Ray Reflection Spectra, A. C. Fabian, D. R. Wilkins, J. M. Miller, R. C. Reis, C. S. Reynolds, E. M. Cackett, M. A. Nowak, G. G. Pooley, K. Pottschmidt, J. S. Sanders, R. R. Ross, J. Wilms Jul 2012

On The Determination Of The Spin Of The Black Hole In Cyg X-1 From X-Ray Reflection Spectra, A. C. Fabian, D. R. Wilkins, J. M. Miller, R. C. Reis, C. S. Reynolds, E. M. Cackett, M. A. Nowak, G. G. Pooley, K. Pottschmidt, J. S. Sanders, R. R. Ross, J. Wilms

Physics and Astronomy Faculty Research Publications

The spin of Cygnus X-1 is measured by fitting reflection models to Suzaku data covering the energy band 0.9-400 keV. The inner radius of the accretion disc is found to lie within 2 gravitational radii (rg=GM/c2), and a value of ? is obtained for the dimensionless black hole spin. This agrees with recent measurements using the continuum fitting method by Gou et al. and of the broad iron line by Duro et al. The disc inclination is measured at ?, which is consistent with the recent optical measurement of the binary system inclination by Orosz et …


Findchirp: An Algorithm For Detection Of Gravitational Waves From Inspiraling Compact Binaries, Bruce Allen, Warren G. Anderson, Patrick R. Brady, Duncan A. Brown, Jolien D E Creighton Jun 2012

Findchirp: An Algorithm For Detection Of Gravitational Waves From Inspiraling Compact Binaries, Bruce Allen, Warren G. Anderson, Patrick R. Brady, Duncan A. Brown, Jolien D E Creighton

Physics - All Scholarship

Matched-filter searches for gravitational waves from coalescing compact binaries by the LIGO Scientific Collaboration use the FINDCHIRP algorithm: an implementation of the optimal filter with innovations to account for unknown signal parameters and to improve performance on detector data that has nonstationary and non-Gaussian artifacts. We provide details on the FINDCHIRP algorithm as used in the search for subsolar mass binaries, binary neutron stars, neutron star-black hole binaries, and binary black holes.


Orbital Velocities In The Broad Line Region Of Seyfert 1 Galaxies, Rebecca Renee Rosen Jun 2012

Orbital Velocities In The Broad Line Region Of Seyfert 1 Galaxies, Rebecca Renee Rosen

Physics

Active galactic nuclei (AGNs) are among the most energetic objects in the Universe and are believed to be powered by supermassive black holes. By studying optical spectra of these AGNs, information can be acquired about the central black hole and its surroundings. Specifically the broad component of the Hβ emission line can be used to find the velocity of gas in the broad line region, a necessary step in determining the mass of the central black hole. In this thesis, I present the results of using a python code to measure the broad component of Hβ in the spectra of …


Non-Gaussian Features Of Primordial Magnetic Fields In Power-Law Inflation, Leonardo Motta, Robert R. Caldwell May 2012

Non-Gaussian Features Of Primordial Magnetic Fields In Power-Law Inflation, Leonardo Motta, Robert R. Caldwell

Dartmouth Scholarship

We show that a conformal-invariance–violating coupling of the inflaton to electromagnetism produces a cross correlation between curvature fluctuations and a spectrum of primordial magnetic fields. According to this model, in the case of power-law inflation, a primordial magnetic field is generated with a nearly flat power spectrum and rms amplitude ranging from nG to pG. We study the cross correlation, a three-point function of the curvature perturbation, and two powers of the magnetic field, in real and momentum space. The cross-correlation coefficient, a dimensionless ratio of the three-point function with the curvature-perturbation and magnetic-field power spectra, can be several orders …


Exploring The Possibility Of Floating Orbits For Extreme Mass Ratio Binary Black Holes, Shasvath Jagat Kapadia May 2012

Exploring The Possibility Of Floating Orbits For Extreme Mass Ratio Binary Black Holes, Shasvath Jagat Kapadia

Graduate Theses and Dissertations

A binary black hole system, where each black hole orbits the system's center of mass, loses energy by emission of gravitational waves. This causes both black holes to spiral in towards each other. However, if the binary were to, by some mechanism, gain orbital energy at the same rate that it radiates away this energy, a non-decaying or “floating” orbit would result. The thesis uses superradiant scattering and tidal friction, which are two equivalent ways of looking at a process by which the system can gain orbital energy from the spin energy of either black hole, to determine the possibility …


Hadamard Renormalization Of The Stress Energy Tensor In A Spherically Symmetric Black Hole Space-Time With An Application To Lukewarm Black Holes, Cormac Breen, Adrian Ottewill Apr 2012

Hadamard Renormalization Of The Stress Energy Tensor In A Spherically Symmetric Black Hole Space-Time With An Application To Lukewarm Black Holes, Cormac Breen, Adrian Ottewill

Articles

We consider a quantum field which is in a Hartle-Hawking state propagating in a spherically symmetric black hole space-time. We calculate the components of the stress tensor, renormalized using the Hadamard form of the Green's function, in the exterior region of this space-time. We then specialize these results to the case of the `lukewarm' Riessner-Nordstrom-de Sitter black hole.


Swift Follow-Up Observations Of Unclassified Asca Sources, N. Degenaar, R. L. C. Starling, P. A. Evans, A. P. Beardmore, D. N. Burrows, E. M. Cackett, S. Campana, D. Grupe, A. Moretti, C. Pagani, K. L. Page, V. La Parola, R. Wijnands Apr 2012

Swift Follow-Up Observations Of Unclassified Asca Sources, N. Degenaar, R. L. C. Starling, P. A. Evans, A. P. Beardmore, D. N. Burrows, E. M. Cackett, S. Campana, D. Grupe, A. Moretti, C. Pagani, K. L. Page, V. La Parola, R. Wijnands

Physics and Astronomy Faculty Research Publications

We present Swift follow-up observations of a sample of 35 unclassified faint X-ray sources drawn from the ASCA Galactic centre and Galactic plane surveys. Our short, pointed XRT observations allow detections down to a limiting 0.3-10 keV flux of FX ~ 10-13 erg cm-2 s-1, which translates into a luminosity of LX ~ 1033 erg s-1 for an assumed distance of D = 8 kpc. The brightest source in our sample reaches a maximum 0.3-10 keV luminosity of LX ~ 2 × 1036 (D/8 kpc)2 erg s-1 during …


A Chandra Survey Of Supermassive Black Holes With Dynamical Mass Measurements, Kayhan Gültekin, Edward M. Cackett, Jon M. Miller, Tiziana Di Matteo, Sera Markoff, Douglas O. Richstone Apr 2012

A Chandra Survey Of Supermassive Black Holes With Dynamical Mass Measurements, Kayhan Gültekin, Edward M. Cackett, Jon M. Miller, Tiziana Di Matteo, Sera Markoff, Douglas O. Richstone

Physics and Astronomy Faculty Research Publications

We present Chandra observations of 12 galaxies that contain supermassive black holes (SMBHs) with dynamical mass measurements. Each galaxy was observed for 30 ks and resulted in a total of 68 point-source detections in the target galaxies including SMBH sources, ultraluminous X-ray sources (ULXs), and extragalactic X-ray binaries. Based on our fits of the X-ray spectra, we report fluxes, luminosities, Eddington ratios, and slope of the power-law spectrum. Normalized to the Eddington luminosity, the 2-10 keV band X-ray luminosities of the SMBH sources range from 10-8 to 10-6, and the power-law slopes are centered at ~2 with …


Hadamard Renormalisation Of The Stress Energy Tensor On The Horizons Of A Spherically Symmetric Black Hole Space-Time, Cormac Breen, Adrian Ottewill Mar 2012

Hadamard Renormalisation Of The Stress Energy Tensor On The Horizons Of A Spherically Symmetric Black Hole Space-Time, Cormac Breen, Adrian Ottewill

Articles

We consider a quantum field which is in a Hartle-Hawking state propagating in a general spherically symmetric black hole space-time. We make use of uniform approximations to the radial equation to calculate the components of the stress tensor, renormalized using the Hadamard form of the Green's function, on the horizons of this space-time. We then specialize these results to the case of the `lukewarm' Reissner-Nordstrom-de Sitter black hole and derive some conditions on the stress tensor for the regularity of the Hartle-Hawking state


Non-Equilibrium Landauer Transport Model For Hawking Radiation From A Black Hole, P. D. Nation, M. P. Blencowe, Franco Nori Mar 2012

Non-Equilibrium Landauer Transport Model For Hawking Radiation From A Black Hole, P. D. Nation, M. P. Blencowe, Franco Nori

Dartmouth Scholarship

We propose that the Hawking radiation energy and entropy flow rates from a black hole can be viewed as a one-dimensional (1D), non-equilibrium Landauer transport process. Support for this viewpoint comes from previous calculations invoking conformal symmetry in the near-horizon region, which give radiation rates that are identical to those of a single 1D quantum channel connected to a thermal reservoir at the Hawking temperature. The Landauer approach shows in a direct way the particle statistics independence of the energy and entropy fluxes of a black hole radiating into vacuum, as well as one near thermal equilibrium with its environment. …


Block Preconditioning Of Stiff Implicit Models For Radiative Ionization In The Early Universe, Daniel R. Reynolds, Robert Harkness, Geoffrey So, Michael L. Norman Feb 2012

Block Preconditioning Of Stiff Implicit Models For Radiative Ionization In The Early Universe, Daniel R. Reynolds, Robert Harkness, Geoffrey So, Michael L. Norman

Mathematics Research

No abstract provided.


An Extreme X-Ray Disk Wind In The Black Hole Candidate Igr J17091-3624, A. L. King, J. M. Miller, J. Raymond, A. C. Fabian, C. S. Reynolds, T. R. Kallman, D. Maitra, E. M. Cackett, M. P. Rupen Feb 2012

An Extreme X-Ray Disk Wind In The Black Hole Candidate Igr J17091-3624, A. L. King, J. M. Miller, J. Raymond, A. C. Fabian, C. S. Reynolds, T. R. Kallman, D. Maitra, E. M. Cackett, M. P. Rupen

Physics and Astronomy Faculty Research Publications

Chandra spectroscopy of transient stellar-mass black holes in outburst has clearly revealed accretion disk winds in soft, disk-dominated states, in apparent anti-correlation with relativistic jets in low/hard states. These disk winds are observed to be highly ionized, dense, and to have typical velocities of ~1000 km s-1 or less projected along our line of sight. Here, we present an analysis of two Chandra High Energy Transmission Grating spectra of the Galactic black hole candidate IGR J17091-3624 and contemporaneous Expanded Very Large Array (EVLA) radio observations, obtained in 2011. The second Chandra observation reveals an absorption line at 6.91 ± …


Identifying A New Intermediate Polar Using Xmm-Newton And Integral, Matthew J. Middleton, Edward M. Cackett, Craig Shaw, Gavin Ramsay, Timothy P. Roberts, Peter J. Wheatley Jan 2012

Identifying A New Intermediate Polar Using Xmm-Newton And Integral, Matthew J. Middleton, Edward M. Cackett, Craig Shaw, Gavin Ramsay, Timothy P. Roberts, Peter J. Wheatley

Physics and Astronomy Faculty Research Publications

The bright X-ray source 2XMMi J180438.7-145647 is fortunate to have long baseline observations in INTEGRAL that complement observations taken by other missions. Optical spectroscopy of this object has suggested a distance of ˜7 kpc and an identification with a low-mass X-ray binary. We instead use the X-ray data from 0.3 to 40 keV to identify the source as a bright intermediate polar (IP) with an estimate for the white dwarf mass of ˜0.60 M. This identification is supported by the presence of an iron triplet, the component lines of which are some of the strongest seen in IPs, …


Essentials Of The Theory Of Abstraction - Lecture, Subhajit Kumar Ganguly Jan 2012

Essentials Of The Theory Of Abstraction - Lecture, Subhajit Kumar Ganguly

Subhajit Kumar Ganguly

In not favouring solutions or sets of solutions, the principle of zero-postulation drives away any unwanted incompleteness from the description of the world. It is the interactions between the possible exhaustive set of solutions that creates the impression pointedness or directiveness in the universe, leading to the formation of clusters, as discussed earlier. These interactions may be chaotic in nature, giving rise to attractor points where the directiveness inside any given system asymptotically seem to approach. It is this directiveness, in turn, inside a given system or in the universe as a whole, that is the cause of all known …


Topspin Networks In Loop Quantum Gravity, Christopher L. Duston Jan 2012

Topspin Networks In Loop Quantum Gravity, Christopher L. Duston

Physics Faculty Publications

We discuss the extension of loop quantum gravity to topspin networks, a proposal which allows topological information to be encoded in spin networks. We will show that this requires minimal changes to the phase space, C*-algebra and Hilbert space of cylindrical functions. We will also discuss the area and Hamiltonian operators, and show how they depend on the topology. This extends the idea of 'background independence' in loop quantum gravity to include topology as well as geometry. It is hoped this work will confirm the usefulness of the topspin network formalism and open up several new avenues for research into …


Interacting Dark Energy Models And The Cosmic Coincidence Problem, H. Shojaei, C. Smith, D. Waters Jan 2012

Interacting Dark Energy Models And The Cosmic Coincidence Problem, H. Shojaei, C. Smith, D. Waters

Journal of the Arkansas Academy of Science

Interacting dark energy models have been employed to study the behavior of dark energy and matter in the presence of an interaction between the two. One of the successful aspects of these models is how they explain the cosmic coincidence problem. In this work we consider a specific interaction to study the behavior of dark energy and matter through the history of evolution.


Toward Solving The Cosmological Constant Problem By Embedding, Roman V. Buniy, Thomas W. Kephart Jan 2012

Toward Solving The Cosmological Constant Problem By Embedding, Roman V. Buniy, Thomas W. Kephart

Mathematics, Physics, and Computer Science Faculty Articles and Research

The typical scalar field theory has a cosmological constant problem. We propose a generic mechanism by which this problem is avoided at tree level by embedding the theory into a larger theory. The metric and the scalar field coupling constants in the original theory do not need to be fine-tuned, while the extra scalar field parameters and the metric associated with the extended theory are fine-tuned dynamically. Hence, no fine-tuning of parameters in the full Lagrangian is needed for the vacuum energy in the new physical system to vanish at tree level. The cosmological constant problem can be solved if …


Isometries And Spontaneous Lorentz Violation In General Relativity, Greg Merritt Jan 2012

Isometries And Spontaneous Lorentz Violation In General Relativity, Greg Merritt

Honors Theses

General Relativity, or GR, is a theory which describes gravity as a manifestation of the curvature of space and time. While the other three fundamental forces in nature are represented as field theories, GR is a geometric theory. In the search for a way to reconcile the field theories for the electromagnetic, strong, and weak forces with the gravitational force, a logical place to start is by re-expressing GR as a field theory. In doing so, we find that the theory contains a number of symmetries. When we solve the equations in GR, we find that by choosing certain solutions …