Gravitational Bremsstrahlung in the post-Minkowskian effective field theory

Stavros Mougiakakos (1) , Massimiliano Maria Riva (1) , Filippo Vernizzi (1)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681

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.

Mots clés: higher-order: 0; gravitational radiation: emission; energy spectrum: emission; graviton: production; gravitation: fundamental constant; gravitation: coupling; coupling: linear; tensor: energy-momentum; higher-order: 1; dimension: 1; effective field theory; conservation law; angular momentum; bremsstrahlung; spinless; graviton; Feynman graph; gravitation: weak field; Fourier transformation

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Physique des Hautes Energies - Théorie [hep-th]

Stavros Mougiakakos, Massimiliano Maria Riva, Filippo Vernizzi. Gravitational Bremsstrahlung in the post-Minkowskian effective field theory. Physical Review D, 2021, 104 (2), pp.024041. ⟨10.1103/PhysRevD.104.024041⟩. ⟨hal-03164363⟩