# Scale dependent three-dimensional charged black holes in linear and non-linear electrodynamics

## TL;DR

This paper investigates how scale-dependent couplings affect the properties of charged black holes in (2+1) dimensions within Einstein-Maxwell and Einstein-power-Maxwell theories, analyzing horizon structure and thermodynamics.

## Contribution

It introduces a framework for incorporating scale dependence into black hole solutions in lower-dimensional gravity theories, extending previous static models.

## Key findings

- Scale dependence modifies black hole horizon structures.
- Thermodynamic properties are affected by running couplings.
- Null energy condition constrains the solutions.

## Abstract

In the present work we study the scale dependence at the level of the effective action of charged black holes in Einstein-Maxwell as well as in Einstein-power-Maxwell theories in (2+1)-dimensional spacetimes without a cosmological constant. We allow for scale dependence of the gravitational and electromagnetic couplings, and we solve the corresponding generalized field equations imposing the "null energy condition". Certain properties, such as horizon structure and thermodynamics, are discussed in detail.