https://doi.org/10.1140/epjc/s10052-022-10544-1
Regular Article - Theoretical Physics
All analytic solutions for geodesic motion in axially symmetric space-times
1
Departamento de Matemática Aplicada and Instituto Universitario de Física Fundamental y Matemáticas, Universidad de Salamanca, 37007, Salamanca, Spain
2
Escuela de Física, Universidad Industrial de Santander, Bucaramanga, Colombia
3
Departamento de Física, Universidad de Los Andes, Mérida, Venezuela
Received:
2
April
2022
Accepted:
22
June
2022
Published online:
5
July
2022
Recent observations of the orbits of star clusters around Sgr , imaging of black holes and gravitational waveforms of merging compact objects require a detailed understanding of the general relativistic geodesic motion. We came up with a method to provide all the possible geodesics in an axially symmetric space-time. The Kerr metric is explicitly worked out, recovering the Schwarzschild geodesics in the static limit. We also found the most general Killing tensor and its associated constant of motion for an axisymmetric space-time. The relevance of these results is crucial to understanding the different scenarios and the fundamental nature of the compact object at the galactic center.
The original online version of this article was revised. In this article the acknowledgment was incorrectly given as: LAN gratefully acknowledges the support of the Vicerrectoría de Investigación y Extensión from Universidad Industrial de Santander under project VIE2814.
An erratum to this article is available online at https://doi.org/10.1140/epjc/s10052-022-10607-3.
Copyright comment corrected publication 2022
© The Author(s) 2022. corrected publication 2022
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