https://doi.org/10.1140/epjc/s10052-022-11070-w
Regular Article - Theoretical Physics
Geodesic motion in Euclidean Schwarzschild geometry
1
Department of Physics, University of Vienna, Boltzmanngasse 5, 1090, Vienna, Austria
2
Dipartimento di Fisica “Ettore Pancini”, Complesso Universitario di Monte S. Angelo, Università degli Studi di Napoli “Federico II”, Via Cintia Edificio 6, 80126, Naples, Italy
3
Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Via Cintia Edificio 6, 80126, Naples, Italy
a emmanuele.battista@univie.ac.at, emmanuelebattista@gmail.com
Received:
2
August
2022
Accepted:
23
November
2022
Published online:
2
December
2022
This paper performs a systematic investigation of geodesic motion in Euclidean Schwarzschild geometry, which is studied in the equatorial plane. The explicit form of geodesic motion is obtained in terms of incomplete elliptic integrals of first, second and third kind. No elliptic-like orbits exist in Euclidean Schwarzschild geometry, unlike the corresponding Lorentzian pattern. Among unbounded orbits, only unbounded first-kind orbits are allowed, unlike general relativity where unbounded second-kind orbits are always allowed.
© The Author(s) 2022
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