Geodesic motion in Euclidean Schwarzschild geometry
Emmanuele BattistaDepartment of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, AustriaGiampiero EspositoDipartimento di Fisica "Ettore Pancini", Complesso Universitario di Monte S. Angelo, Università degli Studi di Napoli "Federico II", Via Cintia Edificio 6, 80126 Naples, Italy
2022en
ABI
Abstract
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.
Identifiers
Citations and references
Cited by 110 references