An Effective Field Theory Approach to the Gravitational Two-Body Problem

The aim of this thesis is to introduce the reader on modern gravitational waves physics, showing novel techniques in order to approach the gravitational two-body problem. Given that no exact solution can be found within analytical tools, we will focus on post-Newtonian physics (i.e. deviations from the ordinary Newton’s two body potential) developing an Effective Field Theory approach similar to the Heavy Quark Field Theory in particle physics. Exploiting this scheme, we will derive several Post-Newtonian corrections to the conservative dynamics of a binary system mapping these into multi-loop amplitudes. As original contribution of the present work, it will be presented for the first time the evaluation of a non static 4 PN contribution within amplitude techniques.