Speaker: Giacomo Brunello

Title: Fourier Integrals for Gravitational Radiation

Abstract:

Gravitational radiation emitted during the scattering of two compact objects can be computed directly from scattering amplitudes within the observable-based (KMOC) formalism. In this approach, the gravitational waveform in frequency space is obtained from the Fourier transform of 2→3 scattering amplitudes.

While the momentum-space amplitudes can be evaluated with standard multi-loop techniques, the Fourier transformation to the frequency domain represents a major bottleneck in this computation. In practice, it leads to large intermediate expressions and spurious singularities that obscure the analytic structure of the result.

In this talk, I will describe a framework in which Fourier integrals are treated together with loop integrals as a single class of generalized multi-loop objects. These combined integrals obey integration-by-parts identities and systems of differential equations in the kinematic invariants, allowing one to apply Feynman-integral technology directly to frequency-domain waveforms. 

Using these techniques, we compute the fully analytic next-to-leading-order gravitational waveform in frequency space for the scattering of two compact objects,

together with the numerical emitted power spectrum at next-to-leading-order. 

I will also discuss how this framework opens the way to a systematic study of the associated Fourier differential equations, their solutions in terms of Bessel-like iterated integrals, and asymptotic expansions in relevant kinematic regimes. This provides a route toward higher-precision gravitational-wave predictions, including higher perturbative orders and the incorporation of spin effects.