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arXiv · 2503.23317

Bound-Unbound Universality and the All-Order Semi-Classical Wave Function in Schwarzschild

Majed Khalaf·Chia-Hsien Shen·Ofri Telem
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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 $G$.

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Majed Khalaf, Chia-Hsien Shen, Ofri Telem. 2025-03-30. Bound-Unbound Universality and the All-Order Semi-Classical Wave Function in Schwarzschild. https://arxiv.org/abs/2503.23317

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