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We trained machine learning models on a data set of theoretical gravitational wave templates from the GstLAL matched filtering pipeline. The data set consists of the triggered templates from the matched filtering of injected gravitational waves from the merger of binary black holes. It consideres two different types of gravitational wave injections, spin aligned and spin non-aligned waves. Two different types of models were trained, one on a set of manually constructed features from the GstLAL templates and another on grids of binned templates that exploit the distribution of the triggered templates in their parameter space. These models were found to classify between the spin aligned and spin-non aligned cases with a small but significant accuracy of $0.53$. While poor, this result does point towards the potential of using the otherwise discarded template information of the matched filtering pipeline.

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The first direct observation of gravitational waves by the Laser Interferometer Gravitational Wave Observatory (LIGO) in 2015 was a monumental event. Ever since the need for better processing of the data is needed. This must be done efficiently, i.e. fast and with high enough accuracy. On that account, the idea of using machine learning models is very fascinating as they can identify properties buried in huge amounts of data. The training of such models can be quite intensive, but predictions can be made relatively quickly. Additionally, they allow the compression of a huge reference data set into a smaller machine model [19]. This project serves as a proof of concept where a novel idea is worked out. It aims to combine machine learning with the gravitational wave data processed in LIGO. Normally, one characterizes an observed gravitational wave signal by a single optimal pre-computed waveform, i.e. the most optimal template. The procedure in this project utilizes a distribution of templates for a single observed signal to retain more information. The idea is then to classify two sets of simulations. The first set contains simulated signals which belong to the same family of signals as the templates. For the second set of simulations, this is no longer true as an additional spin effect is introduced. One can confirm that corresponding simulations of the two sets, which only differ in spin, retrieve different template distributions from the LIGO processing pipeline. On a data set, built using the two groups of simulations, classification is performed using a Random Forest model and two Support Vector Machine models. No significant results were obtained. However, the framework behind this project has been worked out and can be used for further analysis.

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Overall, this Master's thesis is located in the field of numerical relativity and has two main goals. It can for that reason be roughly divided into two parts. In the first part, a specific decomposition of spacetime, known as the 3+1 decomposition, is recapped in order to prepare Einstein's equations for numerical simulations. This is non-trivial as our human brains are not well adapted to visualize a four-dimensional space and we naturally find it more easy to visualize spatial surfaces being evolved over some chosen time-like coordinate. Afterwards, it is necessary to show that the resulting set of equations is well-posed. That is, the solution is unique and depends continuously on the initial data. This task proves to be challenging, especially for theories beyond general relativity. Moreover, there is no general scheme to follow; each system must be considered on a case-by-case basis. Therefore, in the first part of this thesis, it is shown that several formulations of Einstein's equations are well-posed (including an alternative theory to general relativity) and the importance of the constraint equations in obtaining a well-posed system is emphasized. The second part embarks on a completely different route compared to the first part. The knowledge gained from the first part is utilized by conducting several simulations of a one-dimensional neutron star in a specific theory beyond general relativity. This is achieved by extending the equations in the existing numerical relativistic code exttt{Gmunu}. The objective in the second part is to observe a phenomenon called spontaneous scalarization, which occurs when an additional gravitational scalar field is coupled to matter. Under certain conditions, the scalar field takes a non-trivial configuration, which turns out to be the most stable state. Since this scalar field vanishes in standard general relativity, the shift in configurations can be potentially measured and is thus of interest to study. Implementing the evolution equations for the scalar fields in exttt{Gmunu} proved to be challenging; they could not be succesfully implemented without encountering issues. Instead, the encountered difficulties are discussed and the effects of treating the scalar fields as constants as an alternative approach are explored. The neutron star is found to be oscillating. Fourier transforms of the central density are performed in order to find the eigenmode frequencies of these oscillations. It is shown that, for standard general relativity, the obtained eigenmode frequencies are in agreement with the known frequencies in the literature. Finally, the effect of constant scalar fields on the eigenmode frequencies is analyzed. By varying a perturbation parameter, it is shown that the eigenmode frequencies that appear in standard general relativity stay approximately the same although the underlying reason of the oscillation has changed. Moreover, when a certain threshold of the perturbation parameter is passed, there appear additional eigenmode frequencies. This is an indication that the neutron star is scalarized.

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Gravitational waves are disturbances that propagate through the very fabric of spacetime, much like the ripples that radiate across a pond when a pebble is tossed in. However, these spacetime waves are generated by the motion of celestial objects, such as two stars orbiting each other and gradually losing energy in the form of these gravitational waves during their orbital dance. As these gravitational waves journey toward us, they can encounter and be influenced by various celestial objects along their path, including galaxies and stars. This phenomenon is known as gravitational lensing. The effect of this bending by the galaxies often leads to multiple images of the source as we look in the sky. These images are what we detect using the relevant instrument. However, this phenomenon of gravitational lensing by galaxies is also influenced by the stars, like Sun that lie closeby to the galaxies. These stellar objects can impact the signals from lensing by galaxies detected by our instruments, potentially introducing complexities in the analysis of these signals. Therefore it is essential to investigate how a population of these stellar objects stars affects the lensed signal from the massive galaxies. To achieve this objective, a code has been developed specifically for simulating the presence of a population of these stellar objects (ranging from 0.08 to 1.5 times the mass of the sun) in close proximity to the massive galaxy (mass ∼ 1010 times the mass of sun). This code builds upon existing methods used to model gravitational lensing caused by a single star. Additionally, two key parameters have been used to systematically quantify the impact of microlensing, changes in which affect the measurement of the parameters one can infer from the Gravitational wave observations. Within the setup of this work, for the signal which is weakly magnified due to lensing by the galaxy lens, it has been found that the population of these stellar mass objects are less likely to significantly impact the measurement of the parameters such as mass and spin of the source producing gravitational waves in the observation. However, the effective amplitude of the original gravitational wave signal lensed by the galaxy is likely to be amplified due to the presence of a population of these stellar mass objects, which holds significant importance in cosmological investigations associated with lensing studies. In addition to the coding related aspect, this research also contributes to the existing literature by systematic quantification of the lensing effects of a population of these stellar mass objects. The insights derived from this thesis and the code developed possess the potential for application in existing literature studies and in the extended exploration of the effect.

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Future detections of gravitational waves originating from binary neutron star mergers or core-collapse supernovae offer the potential to gain unprecedented insights into the structure of matter at densities far beyond those probed by Earth-based experiments. In order to be able to identify the correct equation of state of matter, a template bank of waveforms has to be generated by general relativistic magnetohydrodynamics simulations. However, state-of-the-art solvers are slowed down by the conservative-toprimitive transformation, a central algorithmic step in any relativistic hydrodynamics solver. We investigate the potential of three machine learning algorithms to improve existing conservative-to-primitive schemes. We find that fully replacing either the conservative-to-primitive transformation or the evaluation of the equation of state by a machine learning model is unable to provide any significant advantage. We propose a novel, hybrid scheme that unifies machine learning and state-of-the-art schemes, resulting in an acceleration of numerical solvers by up to 25% for general relativistic magnetohydrodynamics simulations involving microphysical equations of state, without compromising accuracy or robustness.