Gravitational waveform from radial infall at the third-and-half post-Newtonian order

We compute the gravitational waveform associated with a radially infalling particle in a Schwarzschild black hole working in the center-of-mass system and in a post-Newtonian (PN) approximation. Our results reach the highest accuracy level fully displayed in the literature for multipolar post-Minkowskian computations, namely, the 3.5PN order. The latter accuracy includes both conservative and radiation-reaction contributions (at 2.5PN and 3.5PN) in the two-body dynamics, and corresponding effects in the waveform, too. The apparent simplicity of the radial fall (namely, the one-dimensional motion) contrasts with the peculiarity of the process that will end necessarily with the capture of the particle by the black hole, featuring strong-field effects. In other words, our analysis being limited to the region of validity of the PN approximation cannot capture (by definition of PN approximation) the final phase of the fall, but offers significant insights anyway. This work is an extension o