Gravity Waves from Soft Theorem in General Dimensions

TL;DR

This paper connects soft graviton theorems to gravitational wave spectra in general dimensions, providing explicit calculations and generalizations to complex scattering scenarios, with implications for understanding classical gravitational radiation.

Contribution

It extends the classical soft graviton theorem to compute gravitational wave spectra in general dimensions and includes multiple objects and dynamic mass exchange scenarios.

Findings

Computed angular power spectrum of gravitational radiation using soft theorems.

Validated results with explicit classical scattering examples.

Discussed modifications of soft expansion in four dimensions due to infrared divergences.

Abstract

Classical limit of multiple soft graviton theorem can be used to compute the angular power spectrum of long wavelength gravitational radiation in classical scattering provided the total energy carried away by the radiation is small compared to the energies of the scatterers. We could ensure this either by taking the limit in which the impact parameter is large compared to the Schwarzschild radii of the scatterers, or by taking the probe limit where one object (the probe) has mass much smaller than the other object (the scatterer). We compute the results to subsubleading order in soft momentum and test them using explicit examples involving classical scattering. Our analysis also generalizes to the case where there are multiple objects involved in the scattering and the objects exchange mass, fragment or fuse into each other during the scattering. A similar analysis can be carried out for soft photons to subleading order, reproducing standard textbook results. We also discuss the modification of soft expansion in four dimensions beyond the leading order due to infrared divergences.