Physical Sciences and Mathematics Commons^™

Dyonic Taub-Nut-Ads Space Phase Structure, Mohamed Tharwat

Theses and Dissertations

The Taub-NUT spacetime remains to hold many mysteries more than half a century after its discovery. The metric's controversy owes largely to the nut charge and the existence of Misner strings. Traditionally the metric is treated in the euclidean signature, this treatment hides the Misner strings. We treat the Taub-NUT spacetime with the Misner strings visible, not enforcing the time periodicity condition. We examine the phase structure belonging to three different horizon geometries. We deal with the hyperbolic, flat and spherical cases. We consider the stable phases, the phase transitions that exist between them, and find the preferable phases in …

Systematic Study Of Projection Biases In Weak Lensing Analysis, Prudhvi Raj Varma Chintalapati

Graduate Research Theses & Dissertations

The nature of Dark Energy is possibly one of the most fundamental questions in Physicstoday. Comprising 70% of the energy density of the Universe, and being responsible for the accelerated expansion of the Universe, this mysterious form of energy with negative pressure is challenging our current understanding of the fundamental laws of nature. Cosmological parameters like total relative matter Density Ωm, the normalization of power spectrum σ8 and their combination S8 = σ8 (Ωm/0.3)**0.5 are used to quantify our understanding of the evolution of the large-scale structure in the Universe and shed light on the accelerated expansion, caused by the …

Black Holes, Disk Structures, And Cosmological Implications In E-Dimensional Space, Subhash Kak, Menas C. Kafatos

Mathematics, Physics, and Computer Science Faculty Articles and Research

We examine a modern view of the universe that builds on achieved successes of quantum mechanics, general relativity, and information theory, bringing them together in integrated approach that is founded on the realization that space itself is e-dimensional. The global and local implications of noninteger dimensionality are examined, and how it may have increased from the value of zero to its current value is investigated. We find surprising aspects that tie to structures in the universe, black holes, and the role of observations.

Einstein's Equations, Lagrangians For General Relativity, And Adm Formalism, Timothy Corbett

Student Research Submissions

Einstein’s equations describe the relation of spacetime curvature and present matter. We will consider the case of a Lorentzian manifold diffeomorphic to ℝ × Σ, where time t ∈ ℝ and the three-dimensional manifold Σ represents space. In a homogeneous and isotropic universe, the three-dimensional manifold Σ of the Lorentzian manifold has Riemann curvature tensor ⁽³⁾R = KI, where K is a constant and I is the 3 × 3 identity matrix. Space is flat when K = 0, spherical when K is positive, and hyperbolic when K is negative. In this paper, we will show models agreeing with …

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.

Gravitational Wave Timing Residual Models For Pulsar Timing Experiments, Casey Mcgrath

Theses and Dissertations

The ability to detect gravitational waves now gives scientists and astronomers a new way in which they can study the universe. So far, the scientific collaboration LIGO has been successful in detecting binary black hole and binary neutron star mergers. These types of sources produce gravitational waves with frequencies of the order hertz to millihertz. But there do exist other theoretical sources which would produce gravitational waves in different parts of the frequency spectrum. Of these are the theoretical mergers of supermassive black hole binaries (SMBHBs), which could occur upon the merging of two galaxies with supermassive black holes at …

The James Webb Space Telescope And Scientific Progress, Robert Astle

Quest

Independent Research Paper

Research in progress for PHYS 2425: University Physics I

Faculty Mentor: Raji Kannampuzha, Ph.D.

The following paper represents research work done by students in University Physics 2425, the first half of a two-semester introductory course in physics. It is a calculus- based physics course, intended primarily for physics, chemistry, math, and engineering majors. Students are introduced to the concept of academic research by learning to ask research-focused questions and then use the library resources to pursue outside research to find answers. For this assignment, students are asked to investigate a physical science, biological science, or technology problem …

Semiclassical Backreaction On Asymptotically Anti–De Sitter Black Holes, Peter Taylor, Cormac Breen

Articles

We consider a quantum scalar field on the classical background of an asymptotically anti–de Sitter black hole and the backreaction the field’s stress-energy tensor induces on the black hole geometry. The backreaction is computed by solving the reduced-order semiclassical Einstein field equations sourced by simple analytical approximations for the renormalized expectation value of the scalar field stress-energy tensor. When the field is massless and conformally coupled, we adopt Page’s approximation to the renormalized stress-energy tensor, while for massive fields we adopt a modified version of the DeWitt-Schwinger approximation. The latter approximation must be modified so that it possesses the correct …

The Entropic Dynamics Of Relativistic Quantum Fields In Curved Space-Time, Selman Ipek

Legacy Theses & Dissertations (2009 - 2024)

It has often been the case in history that the laws of physics have been used as the framework for understanding and implementing information processing. The tacit assumption is that the laws of physics are fundamental and that the notion of information is derived from these laws. Here we take the opposite view: the laws of physics are an application of the rules for processing information. The inferential framework of entropic dynamics (ED) has previously been developed by A. Caticha for the purposes of understanding and deriving quantum theory, in much the same way that E.T. Jaynes used the MaxEnt …

Spacetime Groups, Ian M. Anderson, Charles G. Torre

All Physics Faculty 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, n), with g being a 4-dimensional Lie algebra and n 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 …

Partial Differential Equations In Curved Spacetimes, Jorge A. Garcia

Theses and Dissertations

It is the ambition of this thesis to analyze in a concise and coherent manner the idiosyncratic nature of partial differential equations and their mathematical structure in distinct curved spacetimes. In our work special interest is taken in quantum fields dwelling within the de-Sitter geometry. In Chapters I, II, III, and IV, a meticulous study of general relativity is undertaken with one of its solutions derived, an introduction of quantum mechanics is posed, the relativistic quantum theory of fermions is defined, and a “merging” of the former chapters and results are considered, respectively. With what has been derived we seek …

Joule's 19th Century Energy Conservation Meta-Law And The 20th Century Physics (Quantum Mechanics And General Relativity): 21st Century Analysis, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

Joule's Energy Conservation Law was the first "meta-law": a general principle that all physical equations must satisfy. It has led to many important and useful physical discoveries. However, a recent analysis seems to indicate that this meta-law is inconsistent with other principles -- such as the existence of free will. We show that this conclusion about inconsistency is based on a seemingly reasonable -- but simplified -- analysis of the situation. We also show that a more detailed mathematical and physical analysis of the situation reveals that not only Joule's principle remains true -- it is actually strengthened: it is …

A Survey Of Dark Matter Candidates And Relations To Particle Physics And General Relativity, Tyler Martell

Honors Program Theses and Projects

Cosmological observations of certain galaxies suggest that the amount of known, measured matter accounted for by the Standard Model of Particle Physics (SM) in those systems is insufficient to account for galactic mechanics (orbital paths and velocities). These observations have led physicists to believe that either General Relativity (GR) is incomplete, or that there exist new sources of yet-to-be detected matter, that may or may not be consistent with SM, called dark matter. Neither GR nor the SM can alone be considered complete theories of the universe for GR is not quantum

mechanical and the SM does not include GR. …

Tests Of General Relativity With Gw170817, B. P. Abbott, R. Abbott, T. D. Abbott, Marco Cavaglia, For Full List Of Authors, See Publisher's Website.

Physics Faculty Research & Creative Works

The recent discovery by Advanced LIGO and Advanced Virgo of a gravitational wave signal from a binary neutron star inspiral has enabled tests of general relativity (GR) with this new type of source. This source, for the first time, permits tests of strong-field dynamics of compact binaries in the presence of matter. In this Letter, we place constraints on the dipole radiation and possible deviations from GR in the post-Newtonian coefficients that govern the inspiral regime. Bounds on modified dispersion of gravitational waves are obtained; in combination with information from the observed electromagnetic counterpart we can also constrain effects due …

Measuring Deterministic And Stochastic Gravitational Waves With Pulsar Timing Array Experiments, Kristina Islo

Theses and Dissertations

Pulsar timing arrays (PTAs) are uniquely poised to detect the nanohertz-frequency gravitational waves from supermassive black hole binaries (SMBHBs) formed during galaxy merger. Efforts are underway to observe three species of gravitational signal from these systems: the stochastic ensemble, individual, adiabatic binary inspirals, and bursts with memory. This dissertation discusses all three.

A typical Bayesian search for evidence of a stochastic gravitational wave background from the superposition of many unresolvable SMBHB inspirals requires weeks to months to deliver results. This is due in part to the inclusion of inter-pulsar spatial and temporal correlations induced in PTA data by such a …

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 …

Gravitational Effects In G -Factor Measurements And High-Precision Spectroscopy: Limits Of Einstein's Equivalence Principle, Ulrich D. Jentschura

Physics Faculty Research & Creative Works

We study the interplay of general relativity, the equivalence principle, and high-precision experiments involving atomic transitions and g-factor measurements. In particular, we derive a generalized Dirac Hamiltonian, which describes both the gravitational coupling for weak fields and the electromagnetic coupling, e.g., to a central Coulomb field. An approximate form of this Hamiltonian is used to derive the leading gravitational corrections to transition frequencies and g factors. The position dependence of atomic transitions is shown to be compatible with the equivalence principle, up to a very good approximation. The compatibility of g-factor measurements requires a deeper subtle analysis in order to …

Search For Tensor, Vector, And Scalar Polarizations In The Stochastic Gravitational-Wave Background, Benjamin P. Abbott, Marco Cavaglia, For Full List Of Authors, See Publisher's Website.

Physics Faculty Research & Creative Works

The detection of gravitational waves with Advanced LIGO and Advanced Virgo has enabled novel tests of general relativity, including direct study of the polarization of gravitational waves. While general relativity allows for only two tensor gravitational-wave polarizations, general metric theories can additionally predict two vector and two scalar polarizations. The polarization of gravitational waves is encoded in the spectral shape of the stochastic gravitational-wave background, formed by the superposition of cosmological and individually unresolved astrophysical sources. Using data recorded by Advanced LIGO during its first observing run, we search for a stochastic background of generically polarized gravitational waves. We find …

A Search For Tensor, Vector, And Scalar Polarizations In The Stochastic Gravitational-Wave Background, Tiffany Summerscales, Ligo Scientific Collaboration And The Virgo Collaboration

Faculty Publications

The detection of gravitational waves with Advanced LIGO and Advanced Virgo has enabled novel tests of general relativity, including direct study of the polarization of gravitational waves. While general relativity allows for only two tensor gravitational-wave polarizations, general metric theories can additionally predict two vector and two scalar polarizations. The polarization of gravitational waves is encoded in the spectral shape of the stochastic gravitational-wave background, formed by the superposition of cosmological and individually-unresolved astrophysical sources. Using data recorded by Advanced LIGO during its first observing run, we search for a stochastic background of generically-polarized gravitational waves. We find no evidence …

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.

Gravitational Radiation From A Toroidal Source, Aidan Schumann

Summer Research

This research uses a linearized form of Einstein's General Relativity to find the quadrupole moment from an oscillating toroidal mass and charge current. With the quadrupole terms, we found the gravitational radiation from the energy distribution. We make the assumptions that we are in the low-energy and far field limits.

Geodesic Structure In Schwarzschild Geometry With Extensions In Higher Dimensional Spacetimes, Ian M. Newsome

Theses and Dissertations

From Birkoff's theorem, the geometry in four spacetime dimensions outside a spherically symmetric and static, gravitating source must be given by the Schwarzschild metric. This metric therefore satisfies the Einstein vacuum equations. If the mass which gives rise to the Schwarzschild spacetime geometry is concentrated within a radius of r=2M, a black hole will form. Non-accelerating particles (freely falling) traveling through this geometry will do so along parametrized curves called geodesics, which are curved space generalizations of straight paths. These geodesics can be found by solving the geodesic equation. In this thesis, the geodesic structure in the Schwarzschild geometry …

First Search For Nontensorial Gravitational Waves From Known Pulsars, Benjamin P. Abbott, Marco Cavaglia, For Full List Of Authors, See Publisher's Website.

Physics Faculty Research & Creative Works

We present results from the first directed search for nontensorial gravitational waves. While general relativity allows for tensorial (plus and cross) modes only, a generic metric theory may, in principle, predict waves with up to six different polarizations. This analysis is sensitive to continuous signals of scalar, vector, or tensor polarizations, and does not rely on any specific theory of gravity. After searching data from the first observation run of the advanced LIGO detectors for signals at twice the rotational frequency of 200 known pulsars, we find no evidence of gravitational waves of any polarization. We report the first upper …

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.

Gw170104: Observation Of A 50-Solar-Mass Binary Black Hole Coalescence At Redshift 0.2, Benjamin P. Abbott, Marco Cavaglia, For Full List Of Authors, See Publisher's Website.

Physics Faculty Research & Creative Works

We describe the observation of GW170104, a gravitational-wave signal produced by the coalescence of a pair of stellar-mass black holes. The signal was measured on January 4, 2017 at 10 11:58.6 UTC by the twin advanced detectors of the Laser Interferometer Gravitational-Wave Observatory during their second observing run, with a network signal-to-noise ratio of 13 and a false alarm rate less than 1 in 70 000 years. The inferred component black hole masses are 31.2_-6.0^+8.4M⊙ and 19.4_-5.9^+5.3M⊙ (at the 90% credible level). The black hole spins are best constrained through measurement of the effective …

Exotic Statistics For Strings In 4d Bf Theory, John C. Baez, Derek K. Wise, Alissa S. Crans

Alissa Crans

After a review of exotic statistics for point particles in 3d BF theory, and especially 3d quantum gravity, we show that string-like defects in 4d BF theory obey exotic statistics governed by the 'loop braid group'. This group has a set of generators that switch two strings just as one would normally switch point particles, but also a set of generators that switch two strings by passing one through the other. The first set generates a copy of the symmetric group, while the second generates a copy of the braid group. Thanks to recent work of Xiao-Song Lin, we can …

Binary Black Hole Mergers In The First Advanced Ligo Observing Run, Benjamin P. Abbott, Marco Cavaglia, For Full List Of Authors, See Publisher's Website.

Physics Faculty Research & Creative Works

The first observational run of the Advanced LIGO detectors, from September 12, 2015 to January 19, 2016, saw the first detections of gravitational waves from binary black hole mergers. In this paper, we present full results from a search for binary black hole merger signals with total masses up to 100M_⊙ and detailed implications from our observations of these systems. Our search, based on general-relativistic models of gravitational-wave signals from binary black hole systems, unambiguously identified two signals, GW150914 and GW151226, with a significance of greater than 5σ over the observing period. It also identified a third possible signal, …

Gw151226: Observation Of Gravitational Waves From A 22-Solar-Mass Binary Black Hole Coalescence, Benjamin P. Abbott, Marco Cavaglia, For Full List Of Authors, See Publisher's Website.

Physics Faculty Research & Creative Works

We report the observation of a gravitational-wave signal produced by the coalescence of two stellar-mass black holes. The signal, GW151226, was observed by the twin detectors of the Laser Interferometer Gravitational-Wave Observatory (LIGO) on December 26, 2015 at 03:38:53 UTC. The signal was initially identified within 70 s by an online matched-filter search targeting binary coalescences. Subsequent off-line analyses recovered GW151226 with a network signal-to-noise ratio of 13 and a significance greater than 5σ. The signal persisted in the LIGO frequency band for approximately 1 s, increasing in frequency and amplitude over about 55 cycles from 35 to 450 Hz, …

Properties Of The Binary Black Hole Merger Gw150914, Benjamin P. Abbott, Marco Cavaglia, For Full List Of Authors, See Publisher's Website.

Physics Faculty Research & Creative Works

On September 14, 2015, the Laser Interferometer Gravitational-Wave Observatory (LIGO) detected a gravitational-wave transient (GW150914); we characterize the properties of the source and its parameters. The data around the time of the event were analyzed coherently across the LIGO network using a suite of accurate waveform models that describe gravitational waves from a compact binary system in general relativity. GW150914 was produced by a nearly equal mass binary black hole of masses 36_-4⁺⁵ M_⊙ and 29_-4⁺⁴M_⊙; for each parameter we report the median value and the range of the 90% credible interval. …

Tests Of General Relativity With Gw150914, Benjamin P. Abbott, Marco Cavaglia, For Full List Of Authors, See Publisher's Website.

Physics Faculty Research & Creative Works

The LIGO detection of GW150914 provides an unprecedented opportunity to study the two-body motion of a compact-object binary in the large-velocity, highly nonlinear regime, and to witness the final merger of the binary and the excitation of uniquely relativistic modes of the gravitational field. We carry out several investigations to determine whether GW150914 is consistent with a binary black-hole merger in general relativity. We find that the final remnant's mass and spin, as determined from the low-frequency (inspiral) and high-frequency (postinspiral) phases of the signal, are mutually consistent with the binary black-hole solution in general relativity. Furthermore, the data following …