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

TL;DR

This paper calculates the gravitational waveform for a particle falling radially into a Schwarzschild black hole using a 3.5PN approximation, including conservative and radiation-reaction effects, providing high-accuracy insights into the process.

Contribution

It presents the highest accuracy 3.5PN order gravitational waveform for radial infall, incorporating both conservative and radiation-reaction effects in the two-body dynamics.

Findings

Achieved 3.5PN order accuracy in waveform calculations.

Included both conservative and radiation-reaction contributions.

Provided insights into the strong-field effects during radial infall.

Abstract

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, 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 1-dimensional motion) contrasts with the peculiarity of the process which 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.