Geodesics in the field of a rotating deformed gravitational source

TL;DR

This paper analyzes equatorial geodesics around a rotating, deformed gravitational source using the Hartle-Thorne metric, deriving analytic expressions and studying effects like frame dragging and quadrupolar deformation.

Contribution

It provides new analytic formulas for orbital parameters and explores the interplay of rotation and oblateness effects on test particle motion.

Findings

Rotation effects can be balanced by quadrupolar deformation effects.

Derived analytic expressions for orbital angular velocity, angular momentum, and energy.

Numerical analysis of frame dragging and deformation influences.

Abstract

We investigate equatorial geodesics in the gravitational field of a rotating and deformed source described by the approximate Hartle-Thorne metric. In the case of massive particles, we derive within the same approximation analytic expressions for the orbital angular velocity, the specific angular momentum and energy, and the radii of marginally stable and marginally bound circular orbits. Moreover, we calculate the orbital angular velocity and the radius of lightlike circular geodesics. We study numerically the frame dragging effect and the influence of the quadrupolar deformation of the source on the motion of test particles. We show that the effects originating from the rotation can be balanced by the effects due to the oblateness of the source.