Constraining quadrupole deformations with relativistic effects

Utepova D. Boshkayev K. Momynov S. Idrissov A. Baimbetova G. Quevedo H. Urazalina A.
September 2025 Springer Nature

European Physical Journal C
2025 #85 Issue 9

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.

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Abai Kazakh National Pedagogical University, Dostyk Ave., 13, Almaty, 050010, Kazakhstan
Al-Farabi Kazakh National University, Al-Farabi Ave., 71, Almaty, 050040, Kazakhstan
Institute of Nuclear Physics, Ibragimova, 1, Almaty, 050032, Kazakhstan
Satbayev University, Satbayev St., 22, Almaty, 050013, Kazakhstan
Fesenkov Astrophysical Institute, Observatory 23, Almaty, 050020, Kazakhstan
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City, Mexico
Dipartimento di Fisica and ICRA, Università di Roma “La Sapienza”, Rome, Italy

Abai Kazakh National Pedagogical University
Al-Farabi Kazakh National University
Institute of Nuclear Physics
Satbayev University
Fesenkov Astrophysical Institute
Instituto de Ciencias Nucleares
Dipartimento di Fisica and ICRA

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