Classical subleading soft graviton theorem in four space-time dimensions determines the gravitational wave-form at late and early retarded time, generated during a scattering or explosion, in terms of the four momenta of the ingoing and outgoing objects. This result was `derived' earlier by taking the classical limit of the quantum soft graviton theorem, and making some assumptions about how to deal with the infrared divergences of the soft factor. In this paper we give a direct proof of this result by analyzing the classical equations of motion of gravity coupled to matter. We also extend the result to the electromagnetic wave-form generated during scattering of charged particles, and present a new conjecture on subsubleading corrections to the gravitational wave-form at early and late retarded time.

中文翻译：

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D = 4 中经典软引力子定理的证明

四个时空维度的经典次导软引力子定理根据进入和离开物体的四个动量确定了在散射或爆炸期间产生的晚期和早期延迟时间的引力波形。这个结果是早先通过采用量子软引力子定理的经典极限，并就如何处理软因子的红外发散做出一些假设而“推导出来的”。在本文中，我们通过分析与物质耦合的重力运动的经典方程来直接证明这一结果。我们还将结果扩展到带电粒子散射过程中产生的电磁波形，并提出了一个新的猜想，即在早期和晚期延迟时间对引力波形进行次俯冲修正。