Gravitational Bremsstrahlung in the post-Minkowskian effective field theory

We study the gravitational radiation emitted during the scattering of two spinless bodies in the post-Minkowskian effective field theory approach. We derive the conserved stress-energy tensor linearly coupled to gravity and the classical probability amplitude of graviton emission at leading and next-to-leading order in the Newton's constant G. The amplitude can be expressed in compact form as one-dimensional integrals over a Feynman parameter involving Bessel functions. We use it to recover the leading-order radiated angular momentum expression. Upon expanding it in the relative velocity between the two bodies v, we compute the total four-momentum radiated into gravitational waves at leading-order in G and up to an order v,(8) finding agreement with what was recently computed using scattering amplitude methods. Our results also allow us to investigate the zero frequency limit of the emitted energy spectrum.