# The three-dimensional general relativistic Poynting-Robertson effect I: radial radiation field

## TL;DR

This paper extends the understanding of the 3D motion of particles under the Poynting-Robertson effect in general relativity, specifically in Kerr spacetime with a radial radiation field, revealing new dynamical behaviors and equilibrium conditions.

## Contribution

It develops the 3D equations of motion for particles in Kerr spacetime under radial radiation, extending previous 2D models, and analyzes the resulting particle dynamics and equilibrium surfaces.

## Key findings

- Particles reach a critical hypersurface where radiation balances gravity.
- Particles with angular momentum drift latitudinally towards the equator.
- Particles without angular momentum stay at fixed latitude on the hypersurface.

## Abstract

In this paper we investigate the three-dimensional (3D) motion of a test particle in a stationary, axially symmetric spacetime around a central compact object, under the influence of a radiation field. To this aim we extend the two-dimensional (2D) version of the Poynting-Robertson effect in General Relativity (GR) that was developed in previous studies. The radiation flux is modeled by photons which travel along null geodesics in the 3D space of a Kerr background and are purely radial with respect to the zero angular momentum observer (ZAMO) frames. The 3D general relativistic equations of motion that we derive are consistent with the classical (i.e. non-GR) description of the Poynting-Robertson effect in 3D. The resulting dynamical system admits a critical hypersurface, on which radiation force balances gravity. Selected test particle orbits are calculated and displayed, and their properties described. It is found that test particles approaching the critical hypersurface at a finite latitude and with non-zero angular moment are subject to a latitudinal drift and asymptotically reach a circular orbit on the equator of the critical hypersurface, where they remain at rest with respect to the ZAMO. On the contrary, test particles that have lost all their angular momentum by the time they reach the critical hypersurface do not experience this latitudinal drift and stay at rest with respects to the ZAMO at fixed non-zero latitude.