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

Abstract

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.

Tidal resonances for fuzzballs

“…They were shown to vanish for Schwarzschild and Kerr BH's [30][31][32] but they are non trivial in higher dimensions, non asymptotically flat spaces, in alternative theories of gravity [33][34][35][36][37][38] and for BH-like compact objects [39,40]. The TLN response of a gravity object codified the mixing between the solutions of the wave equation for a choice of boundary conditions, and it is imprinted in the Post Newtonian (PN) expansion of the gravitational wave signal radiated by a lighter mass inspiraling around it [41]. It shows up at order 5PN beyond the quadrupole approximation, making hard its experimental measure.…”

“…This correspondence exploits the results of Seiberg-Witten (SW) [56], localization [57][58][59] and AGT duality [60], to provide a combinatorial description of the wave functions describing the gravity systems at linear order. In this framework, the Post-Newtonian expansion of the gravitational wave emitted by a particle orbiting around a BH is described by a an instanton sum in a quiver gauge theory, or alternatively as a linear combination of conformal blocks of a two-dimensional CFT [41]. The tidal response is given by a ratio of Gamma functions depending on a single holomorphic function: the quantum SW period a(u, q) with Coulomb branch parameter u and coupling q parametrizing the orbital number and the wave frequency in gravity [47].…”