# Gravitational Lensing of Rays through the Levitating Atmospheres of Compact Objects

## TL;DR

This paper investigates how electromagnetic rays behave when passing through a stable, plasma-supported atmosphere around a compact object, revealing stable orbits and conditions for radiation trapping using general relativity.

## Contribution

It introduces a model of levitating atmospheres around compact objects and analyzes frequency-dependent ray trajectories, including stable orbits and trapping conditions, within a relativistic framework.

## Key findings

- Existence of stable circular orbits within the plasma shell for low-frequency rays
- Identification of families of bound and periodic orbits between the shell and the object
- Conditions for trapping and escape of low-frequency radiation

## Abstract

Electromagnetic rays travel on curved paths under the influence of gravity. When a dispersive optical medium is included, these trajectories are frequency-dependent. In this work we consider the behaviour of rays when a spherically symmetric, luminous compact object described by the Schwarzschild metric is surrounded by an optically thin shell of plasma supported by radiation pressure. Such levitating atmospheres occupy a position of stable radial equilibrium, where radiative flux and gravitational effects are balanced. Using general relativity and an inhomogeneous plasma we find the existence of a stable circular orbit within the atmospheric shell for low-frequency rays. We explore families of bound orbits that exist between the shell and the compact object, and identify sets of novel periodic orbits. Finally, we examine conditions necessary for the trapping and escape of low-frequency radiation.