Classical soft graviton theorem rewritten

Classical soft graviton theorem gives the gravitational wave-form at future null infinity at late retarded time u for a general classical scattering. The large u expansion has three known universal terms: the constant term, the term proportional to 1/u and the term proportional to ln u/u(2), whose coefficients are determined solely in terms of the momenta of incoming and the outgoing hard particles, including the momenta carried by outgoing gravitational and electromagnetic radiation produced during scattering. For the constant term, also known as the memory effect, the dependence on the momenta carried away by the final state radiation / massless particles is known as non-linear memory or null memory. It was shown earlier that for the coefficient of the 1/u term the dependence on the momenta of the final state massless particles / radiation cancels and the result can be written solely in terms of the momenta of the incoming particles / radiation and the final state massive particles. In this note we show that the same result holds for the coefficient of the ln u/u(2) term. Our result implies that for scattering of massless particles the coefficients of the 1/u and ln u/u(2) terms are determined solely by the incoming momenta, even if the particles coalesce to form a black hole and massless radiation. We use our result to compute the low frequency flux of gravitational radiation from the collision of massless particles at large impact parameter.

Automated summary

The classical soft graviton theorem derives the gravitational wave-form for general classical scattering at future null infinity in the late retarded time. The large u expansion reveals three universal terms with coefficients determined solely by the momenta of incoming and outgoing hard particles. The dependence on the momenta of final state radiation/massless particles cancels for the coefficients of 1/u and ln u/u(2) terms, indicating that the result is solely determined by the momenta of incoming particles/radiation and final state massive particles. The result has implications for calculating the low frequency flux of gravitational radiation in the collision of massless particles with large impact parameter.