Effective Field Theory approach to General Relativity and Feynman diagrams for Coalescing Binary Systems

The discovery of gravitational waves (GWs) emitted by a binary coalescing system has oriented the scientific community towards the development and the application of advanced techniques to reveal gravitational waves and to study waveforms, in order to capture the main characteristics of the astrophysical objects that generate them and to discover new features of the gravitational interaction. A binary system composed of two coalescing objects such as black holes or neutron stars and the successive emission of gravitational waves has been studied in General Relativity (GR) following two different, but related, perturbative schemes, which are the Post-Newtonian (PN) and the Post-Minkowskian (PM) approaches, that allow to evaluate GR corrections to the Newtonian potential. In modern gravitational waves physics such calculations are performed adopting an Effective Field Theory (EFT) approach and with the use of Feynman diagrams and modern Multi-loop techniques which are commonly used in Particle physics. The master thesis focus on two different aspects of the EFT of a coalescing binary system in General Relativity, which are studied using Feynman diagrams. During the first part of this project we are considering the issue of hereditary effects in the PN approach. The hereditary influence is the influence of the past evolution of a material system on its present gravitational internal dynamics, and it is due to GWs emitted by the system in the past and subsequently scattered-off the curvature of space-time back into the system. Such radiation terms give unavoidable contributions to the conservative dynamics of a binary system starting from 4 PN order, and it is mandatory to deal appropriately with this kind of processes in order to compute higher order PN corrections. The current state-of-the-Art of the Post-Newtonian approach has reached the 5PN corrections to the Newtonian potential. Independent derivations of the conservative dynamics at such order present different predictions for physical observables, such as the scattering angle, meaning that we have not a complete understanding of the different contributions entering the conservative dynamics. Our aim is to support with alternative techniques the different derivations of the 5PN corrections, analyzing in detail the hereditary terms appearing using both Feynman and Schwinger-Keldysh formalism, paving the way to a derivation of PN corrections at higher order. The first original contribution of this thesis has been the development of a novel computational algorithm that generates and computes hereditary diagrams, in order to obtain the corresponding conservative Lagrangians in Feynman and in Schwinger-Keldysh formalism. It has been used to make an independent derivation of the 5PN hereditary terms, which involved the evaluation of several two-loop amplitudes, and it can be generalized at higher PN order. Moreover, motivated by analogous studies done for other gauge theories such as QED and QCD, in the second part of the project we analyze the problem of the bending of light under the influence of a massive object in the PM approach, which can be seen as a scattering process between one massive and one massless particle in the low-energy effective theory of gravity. Our aim is to investigate additional insights of the gravitational force, by performing high precision predictions of physical observables in this framework. The second original contribution of this thesis has been the development of a computational setup fully automated in Mathematica which evaluates the 1-loop classical and quantum corrections to the bending process in dimensional regularization. By using a novel approach, new relevant quantum terms arise, that were not present in previous analyses, modifying predictions for physical observables. This algorithm has been also adapted to compute classical and quantum 1-loop corrections to the gravitational potential between two compact objects.