Abstract
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.
Highlights
Process in terms of the momenta and spin of the incoming and outgoing objects, without any reference to the interactions responsible for the scattering [15]
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
We 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
Summary
We shall set up some notations and collect some mathematical results that will be used in our analysis. The derivation of these results can be found in appendix A. We begin by setting up our notation for different Fourier transforms that we shall use in our analysis. We shall deal with functions of four variables x ≡ (t, x) ≡ (x0, x1, x2, x3) describing the space-time coordinates. Given any such function F (x), we shall introduce the following different kinds of Fourier transforms:. Eqs. (2.5)–(2.8) have been proved in appendix A.2
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