Constraining quadrupole deformations with relativistic effects

TL;DR

This paper analyzes how quadrupole deformations in spacetime affect relativistic effects like the Shirokov and Shapiro effects using the Zipoy-Voorhees metric, revealing significant impacts on gravitational time delays.

Contribution

It provides a first-order approximation of quadrupole effects on relativistic phenomena within the Zipoy-Voorhees spacetime, extending understanding of non-spherical gravitational fields.

Findings

Quadrupole moments significantly influence the Shapiro time delay.

The source's quadrupole parameter affects geodesic deviation and oscillatory motion.

First-order effects show pronounced impact on gravitational time delay.

Abstract

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.