Abstract
We consider perturbations of the $4$ dimensional Reissner-Nordstr\"om spacetime induced by the probe scattering of a point particle with charge and mass moving on an unbound trajectory with an asymptotically large velocity. The resulting classical radiative solutions are the gravitational and electromagnetic bremmstrahlung. We use these classical solutions to derive the universal photon and graviton soft factor contributions at the tree level, which have the same form as noted in the literature. The soft factor expressions enable us to investigate the tail contribution to the memory effect in late time gravitational and electromagnetic waveforms. We find that generically, the contribution from the charge dominates that from the mass in the late time radiation.
Highlights
The radiation emitted by accelerated particles on curved spacetimes cover an important class of scattering problems in classical general relativity
Solutions include the electromagnetic radiation emitted by point charges [1,2,3] and the gravitational radiation emitted by point masses [4,5] on the Schwarzschild background
Sem and Sgr are the soft factors in the classical limit of the soft graviton theorem and soft photon theorem with the expressions
Summary
The radiation emitted by accelerated particles (bremsstrahlung) on curved spacetimes cover an important class of scattering problems in classical general relativity. This paper is motivated by the results of [70], where it was shown that universal contributions in the photon and graviton soft factors in any spacetime dimensions can be derived from classical electromagnetic and gravitational scattering processes. The low frequency result follows from taking the limit of the sum over moments, which in general is a more cumbersome route to soft limit expressions For these reasons, in this paper we extend the result of [2,4] and consider the scattering of a point particle with mass and charge on the four-dimensional RN spacetime, with the particle velocity taking on asymptotically large values. We subsequently use our classical radiation results to demonstrate that they provide the expected tree-level soft factor involved in the soft photon and graviton theorems, including phases.
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