Trajectory of test particle around a slowly rotating relativistic star emitting isotropic radiation

TL;DR

This paper investigates the motion of test particles near a slowly rotating relativistic star emitting isotropic radiation, revealing the existence of a stable 'suspension orbit' influenced by radiation forces and star properties.

Contribution

It introduces a detailed analysis of test particle trajectories considering radiation effects, highlighting the phenomena of radiation drag and counter-drag in relativistic star environments.

Findings

Existence of a 'suspension orbit' at a radius determined by luminosity and star's angular momentum.

Radiation counter-drag can cause particles to hover with angular velocity exceeding frame-dragging effects.

Radial position of the suspension orbit is independent of initial particle conditions.

Abstract

We explored the motion of test particles near slowly rotating relativistic star having a uniform luminosity. In order to derive the test particle's equations of motion, we made use of the radiation stress-energy tensor first constructed by Miller and Lamb \cite{ML96}. From the particle's trajectory obtained through the numerical integration of the equations of motion, it is found that for sufficiently high luminosity, "suspension orbit" exists, where the test particle hovers around at uniform angular velocity in the same direction as the star's spin. Interestingly, it turned out that the radial position of the "suspension orbit" was determined by the luminosity and the angular momentum of the star alone and was independent of the initial positions and the specific angular momentum of the particle. Also found is that there exist not only the radiation drag but also "radiation counter-drag" which depends on the stellar radius and the angular momentum and it is this radiation counter-drag that makes the test particle in the "suspension orbit" to hover around at uniform angular velocity which is greater than that induced by the Lense-Thirring effect (i.e., general relativistic dragging of inertial frame).