English

Geodesic motion in Euclidean Schwarzschild geometry

General Relativity and Quantum Cosmology 2022-12-01 v3 High Energy Physics - Theory

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.

Keywords

Cite

@article{arxiv.2202.03763,
  title  = {Geodesic motion in Euclidean Schwarzschild geometry},
  author = {Emmanuele Battista and Giampiero Esposito},
  journal= {arXiv preprint arXiv:2202.03763},
  year   = {2022}
}

Comments

v3: version accepted for publication in EPJ C

R2 v1 2026-06-24T09:25:53.440Z