https://doi.org/10.1140/epjc/s10052-025-14664-2
Regular Article - Theoretical Physics
Constraining quadrupole deformations with relativistic effects
1
Abai Kazakh National Pedagogical University, Dostyk Ave., 13, 050010, Almaty, Kazakhstan
2
Al-Farabi Kazakh National University, Al-Farabi Ave., 71, 050040, Almaty, Kazakhstan
3
Institute of Nuclear Physics, Ibragimova, 1, 050032, Almaty, Kazakhstan
4
Satbayev University, Satbayev St., 22, 050013, Almaty, Kazakhstan
5
Fesenkov Astrophysical Institute, Observatory 23, 050020, Almaty, Kazakhstan
6
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City, Mexico
7
Dipartimento di Fisica and ICRA, Università di Roma “La Sapienza”, Rome, Italy
a
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Received:
30
June
2025
Accepted:
21
August
2025
Published online:
15
September
2025
We investigate two general relativistic effects—namely, the Shirokov and Shapiro effects—within the framework of the Zipoy–Voorhees spacetime (q-metric), which generalizes the Schwarzschild solution by incorporating a quadrupole moment. By analyzing the geodesic deviation equations, we explore the oscillatory motion of test particles and demonstrate how the source’s quadrupole parameter influences the Shirokov effect. Furthermore, we derive an expression for the Shapiro time delay in this deformed spacetime and examine the quadrupole moment’s impact on the gravitational time delay experienced by radio waves propagating near a massive object. The first-order approximation reveals a pronounced effect of the quadrupole parameter on the time delay, in contrast to similar recent analyses. These findings deepen our understanding of how deviations from spherical symmetry influence gravitational phenomena, with potential implications for the study of compact astrophysical objects such as neutron stars and naked singularities or “black hole mimickers” that exhibit significant multipolar structures.
© The Author(s) 2025
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