Theses and Dissertations at Montana State University (MSU)
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Item Numerical methods for rotating compact objects in modified gravity theories(Montana State University - Bozeman, College of Letters & Science, 2020) Sullivan, Andrew Patrick Kyung; Chairperson, Graduate Committee: Neil J. Cornish and Nicolas Yunes (co-chair); Nicolas Yunes was a co-author of the article, 'Slowly-rotating neutron stars in massive bigravity' in the journal 'Classical and quantum gravity' which is contained within this dissertation.; Nicolas Yunes, and Thomas Sotiriou were co-authors of the article, 'Numerical black hole solutions in modified gravity theories: spherical symmetry case' in the journal 'Physical review D' which is contained within this dissertation.; Nicolas Yunes, and Thomas Sotiriou were co-authors of the article, 'Numerical black hole solutions in modified gravity theories: axial symmetry case' submitted to the journal 'Physical review D' which is contained within this dissertation.Detailed observations of phenomena involving compact objects will provide us with a new avenue to test general relativity in the strong field regime. So as to not bias our analysis of these new experiments, we require knowledge of the spacetimes around these objects both within and beyond general relativity. Here I will describe work that applies two specific methods to solve the modified Einstein's equations that describe the exotic spacetimes beyond general relativity for neutron stars and black holes. The first method is a fourth-order Runge-Kutta-Fehlberg ordinary differential equation numerical integrator method. The second method is a relaxed Newton- Raphson method applied to a system of nonlinear partial differential equations. Using these methods, we solve for the spacetimes of slowly rotating neutron stars in massive bigravity and rotating black holes in scalar Gauss-Bonnet gravity in a theory independent methodology. We validate our numerical methods by applying them to compact objects in general relativity and using them to recover known perturbative solutions. We can then compare the fully nonlinear solutions to these perturbative solutions and comment on their differences. We then use these numerical solutions to calculate the physical observables of these systems and finally construct analytic fitted models that can be used in rapid computation methods that future experiments may use to constrain the free parameters in these theories.Item Eccentric gravitational waves: modeling and data analysis implications(Montana State University - Bozeman, College of Letters & Science, 2020) Moore, Blake Carroll; Chairperson, Graduate Committee: Nicolas Yunes and Neil J. Cornish (co-chair); Travis Robson, Nicholas Loutrel and Nicolas Yunes were co-authors of the article, 'A Fourier domain waveform for non-spinning binaries with arbitrary eccentricity' in the journal 'Classical and quantum gravity' which is contained within this dissertation.; Nicholas Loutrel was a co-author of the article, 'A 3PN Fourier domain waveform for non-spinning binaries with moderate eccentricity' in the journal 'Classical and quantum gravity' which is contained within this dissertation.; Nicolas Yunes was a co-author of the article, 'Data analysis implications of moderately eccentric gravitational waves' submitted to the journal 'Classical and quantum gravity' which is contained within this dissertation.; Nicolas Yunes was a co-author of the article, 'Constraining gravity with eccentric gravitational waves: projected upper bounds and model selection' submitted to the journal 'Classical and quantum gravity' which is contained within this dissertation.The ground based advanced Laser Interferometer Gravitational wave Observatory (LIGO) has now made numerous detections of compact objects, ushering in an era of gravitational wave astronomy. Soon the Laser Interferometer Space Antenna (LISA) will become operational and allow for even more detections of gravitational waves. With these detections we are able to characterize the physical properties of the sources - the nature of the orbit, the parameters of the individual compact object, and the parameters of the final merged object. Beyond these source measurements, gravitational waves have proven an important test bed for validating General Relativity, as well as testing theoretical astrophysical formation scenarios of these compact binaries. In order to reach these ends, we require accurate and efficient models for the gravitational waves as seen in the detector. While current detections by ground based detectors are consistent with compact binaries in quasi-circular orbits, there are formation scenarios which suggest that some small number of detectable events will be from compact objects in eccentric orbits, and certainly a healthy number of sources detectable by LISA will be in eccentric orbits. We have derived, validated, and explored the data analysis properties of a waveform model for compact objects in eccentric orbits. In the derivation of the waveform we have employed a truncated sum of harmonics, the stationary phase approximation, and a bivariate expansion in eccentricity and orbital velocity. To explore the data analysis implications of this model we have implemented Markov Chain Monte Carlo algorithms to produce the posterior distributions on the waveform parameters. We find that our model is highly accurate for the inspiral phase of compact objects in orbits with eccentricity as high as 0.8, and very computationally efficient - taking only 90ms to evaluate on average. System parameters are best measured when the source eccentricity is about 0.4, sometimes providing two orders of magnitude better measurement than its quasi-circular counterpart, and eccentric signals can provide more stringent constraints on alternative theories of gravity.Item Testing general relativity through the computation of radiative terms and within the neutron star strong-field regime(Montana State University - Bozeman, College of Letters & Science, 2019) Saffer, Alexander; Chairperson, Graduate Committee: Nicolas Yunes; Kent Yagi and Nicolas Yunes were co-authors of the article, 'The gravitational wave stress-energy (pseudo)-tensor in modified gravity' in the journal 'Classical and quantum gravity' which is contained within this thesis.; Nicolas Yunes was a co-author of the article, 'Angular momentum loss for a binary system in Einstein-aether theory' in the journal 'Physical review D' which is contained within this thesis.; Hector O. Silva is an author and Nicolas Yunes is a co-author of the article, 'The exterior spacetime of relativistic stars in scalar-Gauss-Bonnet gravity' submitted to the journal 'Physical review D' which is contained within this thesis.The recent detection of coalescing black holes by the Laser Interferometer Gravitational-wave Observatory has brought forth the era of gravitational wave astronomy. Physicists are only now beginning to probe the mergers of compact objects that send ripples through space and time. These distortions carry with them the information from the system where they originated. The dynamics of black hole collisions and neutron star mergers are new and exciting events which were undetectable just a few years ago. Einstein's theory of General Relativity has done an excellent job of describing gravity and the information that can be extracted from gravitational systems. However, his theory contains several anomalies such as the inability to explain the inflation of the universe, the effects of dark matter and energy, the presence of singularities, as well as a failure to reconcile with quantum mechanics. Modified theories of gravity have been proposed to answer any remaining questions about gravitation while prescribing solutions to the problems General Relativity still has. The work within this thesis describes how we may study modified theories of gravity in the strong field regime through two different means. The first, is through the calculation of the rate of gravitational radiation from binary systems. This rate varies depending on the theory of gravity being studied. Comparing the theoretical predictions of these rates from alternative theories to astronomical observation will allow us to place better constraints on modified gravity and test General Relativity like never before. The second way is through the investigation of the spacetime surrounding a neutron star. Unlike black holes which emit no light, we are able to see neutron stars (more specifically pulsars) through their light curve as they rotate. The shape of the light curve is dictated by the theory of gravitation used to describe the spacetime around the neutron star. My goal of constructing such a spacetime for neutron stars in modified gravity allows for future scientists to study the light curves to be detected and place constraints on the particular theory.Item Global analysis for space-based gravitational wave observatories(Montana State University - Bozeman, College of Letters & Science, 2018) Robson, Travis James; Chairperson, Graduate Committee: Neil J. Cornish; Nicolas Yunes (co-chair); Neil Cornish and Chang Liu were co-authors of the article, 'The construction and use of LISA sensitivity curves' submitted to the journal 'Classical and quantum gravity' which is contained within this thesis.; Neil Cornish was a co-author of the article, 'Impact of galactic foreground characterization on a global analysis for the LISA gravitational wave observatory' in the journal 'Classical and quantum gravity' which is contained within this thesis.; Neil Cornish, Nicola Tamanini and Silvia Toonen were co-authors of the article, 'Detecting hierarchical stellar systems with LISA' in the journal 'Physical Review D' which is contained within this thesis.; Travis Robson, Blake Moore, Nicholas Loutrel and Nicolas Yunes were all authors of the article, 'A fourier domain waveform for non-spinning binaries with arbitrary eccentricity' in the journal 'Classical and quantum gravity' which is contained within this thesis.; Neil Cornish was a co-author of the article, 'Detecting gravitational wave bursts with LISA in the presence of instrumental glitches' submitted to the journal 'Physical review D' which is contained within this thesis.; Dissertation contains one article of which Travis Robson is not the main author.The Laser Interferometer Space Antenna (LISA) is a space-based gravitational wave detector in development under a joint venture between ESA and NASA. LISA will be sensitive to a wealth of signals from a variety of sources--both astrophysical and instrumental. Since many of these signals will be overlapping we must carry out a global analysis where we model everything believed to be present in the data simultaneously. To analyze the data this way we must understand what types of signals we expect, develop fast signal generators, and develop data analysis algorithms to handle this problem. We must also be flexible to characterize signals that we do not expect such as instrumental glitches of unknown morphology, or exotic astrophysical sources. We employ the Markov Chain Monte Carlo algorithm to address these multiple facets of the global analysis problem through a Bayesian approach. We have developed fast models for a variety of sources, characterized what we can learn about the sources, and assessed the nature of LISA's global analysis problem.Item Constraining scalar-tensor theories of gravity through observations(Montana State University - Bozeman, College of Letters & Science, 2018) Anderson, David Sutton; Chairperson, Graduate Committee: Nicolas Yunes; Nicolas Yunes and Enrico Barausse were co-authors of the article, 'The effect of cosmological evolution on solar system constraints and on the scalarization of neutron stars in massless scalar-tensor theories' in the journal 'American physical society' which is contained within this thesis.; Nicolas Yunes was a co-author of the article, 'Solar system constraints on massless scalar-tensor gravity with positive coupling constant upon cosmological evolution of the scalar field' in the journal 'American physical society' which is contained within this thesis.; Nicolas Yunes was a co-author of the article, 'Scalar charges and scaling relations in massless scalar-tensor theories' submitted to the journal 'Classical quantum gravity' which is contained within this thesis.; Paulo Freire and Nicolas Yunes were co-authors of the article, 'Binary pulsar constraints on massless scalar-tensor theories using bayesian statistics' submitted to the journal 'Classical quantum gravity' which is contained within this thesis.Scalar-tensor theories of gravity have been among the most popular and well-studied alternatives to Einstein's General Relativity. These theories of gravity contain an extra scalar degree of freedom that allows them to rectify some of the limitations of General Relativity but also fail some of the cornerstone tests of gravity that General Relativity passes with flying colors. Because of these conflicting features, it becomes necessary to investigate if scalar-tensor theories can pass current tests of gravity while still allowing for possible deviations from General Relativity in regimes that are not as highly constrained. In this thesis, we present the first self-consistent study of scalar-tensor theories in which we study the effects and constraints from Solar System observations, cosmological evolution of the universe, and the precise timing of binary pulsar systems. We constrain the free parameters of a certain class of massless-scalar-tensor theories first through cosmology and Solar System tests, in which we investigate the consistency between cosmological evolution scenarios and current Solar System observations. We then study strong field tests involving binary pulsar systems and investigate the various constraints that can be placed from measurements of the Keplerian and post-Keplerian parameters that determine the orbits.Item Eccentric compact binaries: modeling the inspiral and gravitational wave emission(Montana State University - Bozeman, College of Letters & Science, 2018) Loutrel, Nicholas Peter; Chairperson, Graduate Committee: Neil J. CornishThe modeling of the inpsiral and subsequent gravitational wave emission from black hole binary systems has been a long outstanding problem in astrophysics and relativity. Astrophysical models predict that most binaries will have low orbital eccentricity by the time the gravitational wave emission enters the detection band of ground based detectors, and significant success has been made by restricting attention to the this limit, where the binary's orbit is approximately circular. However, exotic formation channels in globular clusters and galactic nuclei predict a small, but non-negligible, fraction of systems will enter the detection band of ground-based detectors with significant orbital eccentricity. In this thesis, we present new methods of modeling eccentric binaries under the influence of gravitational wave emission, focusing on two regimes: (i) the early inspiral of highly eccentric binaries, and (ii) the late inspiral of generic eccentric binaries.Item Black hole electromagnetic observations as tests of general relativity: quadratic gravity(Montana State University - Bozeman, College of Letters & Science, 2017) Ayzenberg, Dimitry; Chairperson, Graduate Committee: Nicolas Yunes; Kent Yagi and Nicolas Yunes were co-authors of the article, 'Linear stability analysis of dynamical quadratic gravity' in the journal 'Physical review D' which is contained within this thesis.; Nicolas Yunes was a co-author of the article, 'Slowly rotating black holes in Einstein-dilaton-Gauss-Bonnet gravity: quadratic order in spin solutions' in the journal 'Physical review D' which is contained within this thesis.; Kent Yagi and Nicolas Yunes were co-authors of the article, 'Can the slow-rotation approximation be used in electromagnetic observations of black holes?' in the journal 'Classical and quantum gravity' which is contained within this thesis.; Nicolas Yunes was a co-author of the article, 'Black hole continuum spectra as a test of general relativity: quadratic gravity' submitted to the journal 'Classical and quantum gravity' which is contained within this thesis.The recent detections of gravitational waves from merging black holes by advanced LIGO provide the first tests of General Relativity that probe the non-linear and dynamical nature of gravity. For General Relativity to be properly tested, though, many more observations are necessary. This lack of tests, coupled with several reasons General Relativity may not be the correct description of nature, motivates the study of modified theories of gravity. This dissertation presents the results of four studies on two well-motivated modified gravity theories in the class known as quadratic gravity: dynamical Chern-Simons gravity and Einstein-dilaton-Gauss-Bonnet gravity. First, I study the stability of quadratic gravity to linear perturbations. If the theory shows instabilities, black holes may not be realized in Nature, and the theory would lack physical motivation. I perform a linear stability analysis, concentrating on dynamical Chern-Simons gravity and Einstein-dilaton-Gauss-Bonnet gravity, and find that these two theories are stable to linear perturbations far from the gravitational source. Exact analytic solutions for rotating black holes in Einstein-dilaton-Gauss-Bonnet gravity are lacking, and most solutions are either numerical or approximate. I expand on previous work and find a new approximate rotating black hole solution to quadratic order in the spin angular momentum. The properties of this new solution are then studied. Many modified gravity theories lack exact solutions for rotating black holes and the approximate nature of those solutions may introduce systematic error in any attempts to constrain those theories using black hole observations. I determine the systematic error introduced by using an approximate black hole solution in General Relativity in the context of continuum spectrum and black hole shadow observations. I find that for small enough values of the spin angular momentum, the systematic error introduced is negligible compared to current sources of observational error. Finally, I study if it is possible to place better-than-current constraints on dynamical Chern-Simons gravity and Einstein-dilaton-Gauss-Bonnet gravity using black hole continuum spectrum observations. I find that while dynamical Chern-Simons gravity cannot be better constrained, with next generation telescopes it may be possible to place better constraints on Einstein-dilaton-Gauss-Bonnet gravity.Item Numerical analysis of bubble nucleation processes for first-order phase transitions within quantum fields(Montana State University - Bozeman, College of Letters & Science, 1991) Samuel, David AdrianItem Space-based gravitational wave astrophysics(Montana State University - Bozeman, College of Letters & Science, 1999) Larson, Shane L.Item Uniformly accelerated solutions of Einstein's equations(Montana State University - Bozeman, College of Letters & Science, 1983) Henline, Timothy James