https://doi.org/10.1140/epjc/s10052-025-13969-6
Regular Article - Theoretical Physics
Geodesic deviation in the q-metric
1
Department of Physics, Nazarbayev University, Kabanbay Batyr 53, 010000, Astana, Kazakhstan
2
Fesenkov Astrophysical Institute, Observatory 23, 050020, Almaty, Kazakhstan
3
Al-Farabi Kazakh National University, Al-Farabi Ave., 71, 050040, Almaty, Kazakhstan
4
Institute of Nuclear Physics, Ibragimova, 1, 050032, Almaty, Kazakhstan
5
Department of Mathematics and Computer Science, Transilvania University of Brasov, 500091, Brasov, Romania
6
Abai Kazakh National Pedagogical University, Dostyk Av., 13, 050010, Almaty, Kazakhstan
Received:
17
January
2025
Accepted:
18
February
2025
Published online:
20
March
2025
We consider the tidal forces between test particles falling along geodesics in the exterior spacetime generated by a static and axially symmetric compact matter source with a non-vanishing mass quadrupole. Specifically, we analyze the radial and angular geodesic deviation, compare it with that of the Schwarzschild spacetime, and investigate the impact of the deformation parameter q at different polar angles (
) with respect to the vertical symmetry axis. Furthermore, we examine the geodesic deviation for the case of non-constant during the radial fall. We show that the presence of the deformation parameter affects the behavior of the geodesic deviation vectors, depending on its value. In particular, we observe that for arbitrary values of q and , the behavior of the deviation vector differs as it approaches the singularity at 
. Above all, we can witness either stretching or compression of the deviation vector for various combinations of q and . These findings provide insight into the effects of quadrupole deformation on the motion of test particles in the vicinity of the central object.
© The Author(s) 2025
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3.
