Shirokov and Shapiro Effects in the Hartle-Thorne Spacetime

TL;DR

This paper analyzes how rotation and quadrupole deformation of compact objects influence the Shirokov and Shapiro effects in the Hartle-Thorne spacetime, combining analytical and numerical methods to reveal their impact on relativistic observables.

Contribution

It provides a detailed analysis of the combined effects of angular momentum and quadrupole moments on Shirokov and Shapiro phenomena without relying on weak-field approximations.

Findings

Both angular momentum and quadrupole moments significantly affect the Shirokov effect.

Oblate sources with higher quadrupole moments produce stronger gravitational time delays.

Numerical analysis confirms the influence of deformation and rotation on relativistic observables.

Abstract

We investigate the influence of rotation and quadrupole deformations of astrophysical compact objects on the Shirokov and Shapiro effects within the Hartle-Thorne spacetime, which describes the exterior gravitational field of slowly rotating, slightly deformed celestial objects. Using geodesic deviation equations, we analyze the oscillatory motion of neighboring test particle trajectories and show how the combined impact of angular momentum $J$ and quadrupole moment $Q$ affects the Shirokov effect. The results are compared with our previous analysis for the Lense-Thirring and Zipoy-Voorhees metrics, revealing consistent trends in the coupling between radial and azimuthal oscillations. For the Shapiro time delay, we examine two limiting configurations: (i) the Lense-Thirring frame-dragging case with $J^2=0$, $Q=0$ and $J\neq0$, where the effect persists for both positive and negative values of the angular momentum; and (ii) the static quadrupolar case with $J=0$ and $Q\neq0$, where more oblate sources produce a stronger gravitational time delay with increasing distance. We also study these effects in the Hartle-Thorne spacetime without employing the weak-field approximation, performing a full numerical analysis. In particular, we examine the mimicking effects produced by the quadrupole deformation and the angular momentum of the compact object. These results illustrate how the deformation and rotation of compact objects influence the relativistic observables in the surrounding spacetime.