# Photons trajectories on a first order scale-dependent static BTZ black hole

## TL;DR

This paper investigates the trajectories of photons around a scale-dependent static BTZ black hole, revealing differences from classical solutions due to the scale-dependent gravity parameter.

## Contribution

It provides analytic solutions for photon trajectories in a scale-dependent BTZ black hole, highlighting deviations from classical gravity models.

## Key findings

- Photon paths differ from classical solutions due to scale dependence.
- Analytic equations of motion are derived for massless particles.
- Differences become evident when comparing to classical BTZ black hole trajectories.

## Abstract

In this paper we study the motion of massless particles on a static BTZ black hole background in the context of scale-dependent gravity, which is characterized by the running parameter $\epsilon$. Thus, by using standard methods we obtain the equation of motions and then analytic solutions are found. The relevant non-trivial differences appear when we compare our solution against the classical counterpart.