In the Zipoy-Voorhees spacetime, the Shapiro time delay and the Shirokov oscillation frequencies acquire corrections from the quadrupole deformation parameter q, with the delay correction appearing at first order in q.
Geodesics in the Gamma spacetime
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Circular and radial geodesics are studied in the spacetime described by the $\gamma$ metric. Their behaviour is compared with the spherically symmetric situation, bringing out the sensitivity of the trajectories to deviations from spherical symmetry.
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Constraining quadrupole deformations with relativistic effects
In the Zipoy-Voorhees spacetime, the Shapiro time delay and the Shirokov oscillation frequencies acquire corrections from the quadrupole deformation parameter q, with the delay correction appearing at first order in q.