# Shadow of a black hole surrounded by dark matter

## TL;DR

This paper derives a formula for the black hole shadow radius considering surrounding dark matter, showing that dark matter can significantly alter the shadow size if concentrated near the black hole.

## Contribution

It provides a simple spherical model to quantify how dark matter influences the size of a black hole's shadow, extending previous Schwarzschild-based analyses.

## Key findings

- Dark matter can significantly affect the shadow size if concentrated near the black hole.
- The effective radius of the dark matter halo influences the shadow, especially when it exceeds rom the photon sphere.
- Dark matter outside the photon sphere becomes important at larger deviations from the Schwarzschild case.

## Abstract

We consider a simple spherical model consisting of a Schwarzschild black hole of mass $M$ and a dark matter of mass $\Delta M$ around it. The general formula for the radius of black-hole shadow has been derived in this case. It is shown that the change of the shadow is not negligible, once the effective radius of the dark matter halo is of order $\sim \sqrt{3 M \Delta M}$. For this to happen, for example, for the galactic black hole, the dark matter must be concentrated near the black hole. For small deviations from the Schwarzschild limit, the dominant contribution into the size of a shadow is due to the dark matter under the photon sphere, but at larger deviations, the matter outside the photon sphere cannot be ignored.