# Black Hole Shadows and Invariant Phase Space Structures

## TL;DR

This paper uses dynamical systems theory to connect light rings and phase space structures with black hole shadows and lensing features, demonstrated through analysis of a hairy black hole.

## Contribution

It introduces a novel framework linking invariant phase space structures to observable black hole shadow features, extending understanding of spacetime lensing.

## Key findings

- Light rings correspond to fixed points in phase space.
- Invariant manifolds shape the black hole shadow.
- Analysis of a hairy black hole illustrates the concepts.

## Abstract

Utilizing concepts from dynamical systems theory, we demonstrate how the existence of light rings, or fixed points, in a spacetime will give rise to families of periodic orbits and invariant manifolds in phase space. It is shown that these structures define the shape of the black hole shadow as well as a number of salient features of the spacetime lensing. We illustrate this through the analysis of lensing by a hairy black hole.