Post Newtonian emission of gravitational waves from binary systems: a gauge theory perspective

Using the AGT correspondence and localization, we derive a combinatorial formula for the Post-Newtonian expansion of the wave form describing the gravitational emission from binary systems made of objects of extremely different masses. The results are written as a double instanton series describing the expansion of the gravitational wave at large distances and small velocities, and are tested against previous formulae in the literature for Schwarschild and Kerr black holes at the 5th and 3rd Post Newtonian order respectively beyond the quadrupole approximation. Tidal effects show up in the wave form at the 5th PN order, providing a quantitative measure of sizes and reflectivity properties of the gravity solution.