Bound-Unbound Universality and the All-Order Semi-Classical Wave Function in Schwarzschild
Abstract
We present a systematic method for analytically computing time-dependent observables for a relativistic probe particle in Coulomb and Schwarzschild backgrounds. The method generates expressions valid both in the bound and unbound regimes, namely bound-unbound universal expressions. To demonstrate our method we compute the time-dependent radius and azimuthal angle for relativistic motion in a Coulomb background (relativistic Keplerian motion), as well as the electromagnetic field radiated by a relativistic Keplerian source. All of our calculations exhibit bound-unbound universality. Finally, we present an exact expression for the semi-classical wave function in Schwarzschild. The latter is crucial in applying our method to any time-dependent observable for probe-limit motion in Schwarzschild, to any desired order in velocity and the gravitational constant .
Cite
@article{arxiv.2503.23317,
title = {Bound-Unbound Universality and the All-Order Semi-Classical Wave Function in Schwarzschild},
author = {Majed Khalaf and Chia-Hsien Shen and Ofri Telem},
journal= {arXiv preprint arXiv:2503.23317},
year = {2025}
}