Light rays and wave fronts in strong gravity

TL;DR

This paper reviews the equations governing light propagation near black holes, focusing on how inhomogeneous accretion disks and relativistic effects influence observed signals like X-ray variability, spectral lines, and polarization.

Contribution

It summarizes the fundamental equations used to model light rays and wave fronts in strong gravity environments, emphasizing their application to accretion disk phenomena.

Findings

Inhomogeneous accretion disks produce variable X-ray signals.

Relativistic effects constrain models of spectral lines and polarization.

Geometrical optics approximation aids in understanding light propagation near black holes.

Abstract

Accretion onto black holes often proceeds via an accretion disk or a temporary disk-like pattern. Variability features observed in light curves as well as theoretical models of accretion flows suggest that accretion disks tend to be inhomogeneous -- variety of substructures (clumps) emerge within the flow. Rapid orbital motion of individual clumps then modulates the observed signal in X-rays. Furthermore, changes of spectral lines and polarization properties of the observed signal (or the absence of changes) constrain the models and reveal information about general relativity (GR) effects. In this write-up we summarize the basic equations that have been employed to study light propagation near black holes and to derive the radiation signal that can be expected at a detector within the framework of geometrical optics approximation.