First post-Newtonian correction to gravitational waves produced by compact binaries: How to compute relativistic corrections to gravitational waves using Feynman diagrams

Abstract

The purpose of this thesis is to calculate the relativistic correction to the gravitational waves produced by compact binaries in the inspiral phase. The correction is up to the next to leading order, the so-called first post-Newtonian order (1PN), which are correctional terms proportional to (v/c) 2 compared to leading order, Newtonian, terms.These corrections are well known in the literature, even going beyond the first order corrections, so why is it computed again here? In later years, an alternative approach for computing these terms using effective field theory has emerged. This thesis investigates this approach by replicating it, and attempts to make this approach more accessible to those not familiar with effective field theories.It has been claimed that this approach greatly simplifies the complicated calculations of gravitational waveforms, and even provides the required intuition for 'physical understanding'. By this master student that was found not to be entirely correct. The calculations were made easier for those with a rich background in quantum field theory, but for those who are not well acquainted with quantum field theory this was not the case.It was, however, found to be a worthwhile method as a means for deepening one's understanding of gravity, and might provide a shorter route for some alternative theories of gravity to testable predictions. I would like to thank my supervisor Alex Bentley Nielsen for adhering to my wishes of working on gravitational waves, and as a consequence the numerous hours spent guiding me through this project. Of these hours, I am especially thankful for the time he spent discussing gravity, academia, and physics in general with me. I found these talks motivating and educational, and often the highlight of my week.I would also like to thank the Department of Mathematics and Physics of the University of Stavanger. During the COVID-19 pandemic, the department made the necessary arrangements to let me come visit them, for which I am grateful. The possibility to spend time physically with my supervisor was much appreciated. They welcomed me with open arms, and I thoroughly enjoyed my stay. A special thanks to Germano Nardini for conversations, coffee, and a scoop of ice cream during my visits to Stavanger.I also extend my thanks to my local supervisor, Jens Oluf Andersen, and NTNU for making the formal facilitations need to make this thesis. Especially for granting travel funds for me to visit Stavanger.Lastly, I thank Michelle Angell for proofreading the last draft of this thesis. There may still linger some typos in this document, but had it not been for her, it would have been many more.iii ForwordThis document is for all intents and purposes my master's thesis, but it deviates to some degree from the document that was handed in for the examination.The reason for this is that this document has been updated based on helpful comments from the examiner, Professor David Fonseca Mota, with additional clarifications and purging of typos. This will hopefully make this docu...