Geodesic deviation in the q-metric

Idrissov A. Boshkayev K. Dialektopoulos K.F. Urazalina A. Utepova D.
March 2025 Springer Nature

European Physical Journal C
2025 #85 Issue 3

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 (θ) with respect to the vertical symmetry axis. Furthermore, we examine the geodesic deviation for the case of non-constant θ 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 θ, the behavior of the deviation vector differs as it approaches the singularity at r=2m. Above all, we can witness either stretching or compression of the deviation vector for various combinations of q and θ. These findings provide insight into the effects of quadrupole deformation on the motion of test particles in the vicinity of the central object.

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Department of Physics, Nazarbayev University, Kabanbay Batyr 53, Astana, 010000, Kazakhstan
Fesenkov Astrophysical Institute, Observatory 23, Almaty, 050020, Kazakhstan
Al-Farabi Kazakh National University, Al-Farabi Ave., 71, Almaty, 050040, Kazakhstan
Institute of Nuclear Physics, Ibragimova, 1, Almaty, 050032, Kazakhstan
Department of Mathematics and Computer Science, Transilvania University of Brasov, Brasov, 500091, Romania
Abai Kazakh National Pedagogical University, Dostyk Av., 13, Almaty, 050010, Kazakhstan

Department of Physics
Fesenkov Astrophysical Institute
Al-Farabi Kazakh National University
Institute of Nuclear Physics
Department of Mathematics and Computer Science
Abai Kazakh National Pedagogical University

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