# Dilatonic BTZ black holes with power-law field

## TL;DR

This paper explores the thermodynamical properties and phase transitions of dilatonic BTZ black holes coupled with nonlinear electromagnetic fields in three dimensions, using both classical and geometrical thermodynamics methods.

## Contribution

It introduces a detailed analysis of thermodynamics and phase transitions of dilatonic BTZ black holes with power-law fields, highlighting the effects of various parameters.

## Key findings

- Temperature and heat capacity behaviors are characterized.
- Phase transition points are identified and analyzed.
- Geometrical thermodynamics confirms the nature of interactions.

## Abstract

Motivated by low energy effective action of string theory and large applications of BTZ black holes, we will consider minimal coupling between dilaton and nonlinear electromagnetic fields in three dimensions. The main goal is studying thermodynamical structure of black holes in this set up. Temperature and heat capacity of these black holes are investigated and a picture regarding their phase transitions is given. In addition, the role and importance of studying the mass of black holes is highlighted. We will see how different parameters modify thermodynamical quantities, hence thermodynamical structure of these black holes. In addition, geometrical thermodynamics is used to investigate thermodynamical properties of these black holes. In this regard, the successful method is presented and the nature of interaction around bound and phase transition points is studied.