Analytic One-loop Scattering Waveform in General Relativity

TL;DR

This paper derives an analytic expression for the scattering waveform in General Relativity at second order and all velocities, enabling efficient numerical evaluation and power spectrum computation of gravitational radiation.

Contribution

It presents a new analytic representation of the next-to-leading order scattering waveform in GR, extending to all velocities and facilitating numerical analysis.

Findings

Analytic waveform derived to second order in G and all velocities.

Power spectrum of gravitational radiation computed to order G^4.

Waveform representation is suitable for numerical evaluation.

Abstract

Leveraging the computational framework presented in reference [JHEP 07, 062 (2024)], we evaluate the analytic scattering waveform in General Relativity to second order, $G^3 M^3 /r b^2$ and to all orders in velocity. This new representation of the next-to-leading order waveform is well-suited for numerical evaluation. Integrating the [modulus square of the] waveform over the angles on the celestial sphere, we also compute the power spectrum of the radiation to order $G^4$ numerically.