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.
Highlights
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
Independent of the theory or the type of particles we have in the external state, and is sensitive only to the momenta and angular momenta carried by these particles
Our analysis further shows that the first step in this relation — the relation between soft theorem and the classical radiative field — is based not on single soft graviton theorem but multiple soft graviton theorem, and relies on the vanishing of the contact term in the multiple soft theorem in the classical limit
Summary
If the macroscopic objects have energies that are comparable to each other, eq (1.4). It was argued in [16, 84, 86, 91, 92] that soft graviton theorem is related to memory effect [93,94,95,96].
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