Abstract
Einstein’s equations of General Relativity were first published in 1915 and are until this day the most accurate understanding of gravity. Although first attempts at using computers to solve them were made in the 1960s [4], only recently has Numerical Relativity (NR) produced mature tools. These new tools came to existence not only due to the recent development of robust numerical techniques but also due to the exponential growth of computational power. A crucial event for NR was the first measurement of two Black holes inspiraling and merging by the LIGO/Virgo collaboration [5] for which numerical simulations played a significant role. This was a technically challenging system to model that required numerical simulations [6–8], and to date, NR is the only tool that can accurately solve it.In this thesis, we study compact objects using Numerical Relativity. In particular, we use NR to investigate the nature and the different possible ways of detecting two strongly gravitating objects: cosmic strings and Boson stars. A better understanding of these objects is essential as they might produce gravitational waves that allow them to be measured by current and future gravitational wave detectors.
An introduction to the different types of Boson stars, with different field-content, different charge or rotating stars, and an overview of the current literature regarding the challenges of measuring and modelling Boson stars is provided on chapter 1. A small introduction to cosmic strings is provided in chapter 5.
Chapter 2 focus on one type of Boson stars, which are made from a single real scalar (i.e. oscillatons) and investigate how changing the potential to the one of an axion can affect its stability. Changing the potential is essential to elucidate if Bosonic stars might be made from dark matter. Our results show that under certain condition the star can collapse into a Black hole or disperse completely.
We study the formation of oscillatons in chapter 3, we simulate sinusoidal initial data and determine whether they collapse to stars. We find that depending on the mass of the perturbation, we can either form Black holes or stable Boson stars. We use this information to create a population of Black holes and Axion stars, binaries of which could be potentially detected by LIGO/Virgo detectors. Chapter 4 explores oscillatons head-on merger. The end product of such mergers can be either a stable, but very perturbed oscillaton or a Black hole. We find that in both cases, the signal is different from a Black hole merger, even if cases where the final result was a Black hole, thus making them a potentially easily differentiable source.
On the other hand, in chapter 5, we study the physics and the gravitational waves produced by Abelian-Higgs cosmic strings. These strings are topological defects that might have formed in the very early universe and can be visualised as long filaments, which move similarly to long rubber bands in zero gravity. Interestingly, they were already predicted by grand unified theories (GUTs), which unifies weak, strong, electromagnetic and gravitational forces. As shown by [9], due to their motion, they might produce gravitational waves, we discuss these findings in this chapter, simulate a collapsing string and extract the gravitational waves emitted by it.
Many new gravitation wave detectors are in the pipeline to be finished in the next few decades. These new detectors will drastically change our ability to probe the universe, allowing us to state more complex questions, and certainly lead to new discoveries of the wonders of our universe. I hope that in this thesis, I set out the path to allow the discovery of two such objects, cosmic strings and oscillatons. There is further work to be done, not only improving on the simulations of oscillatons or cosmic strings but also further developing theories that can then be tested using these future detectors.
| Date of Award | 1 Jul 2020 |
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| Original language | English |
| Awarding Institution |
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| Supervisor | Eugene Lim (Supervisor) & Malcolm Fairbairn (Supervisor) |