# Non-linear black holes in 2+1 dimensions as heat engines

## TL;DR

This paper investigates the thermodynamics and heat engine efficiency of two regular non-linear black holes in 2+1 dimensions, revealing how non-linear parameters and charge influence efficiency.

## Contribution

It introduces a renormalization parameter for thermodynamic consistency and analyzes black hole heat engines, comparing their efficiency to charged BTZ black holes.

## Key findings

- Efficiency increases with non-linear parameter and charge.
- Regular black holes have lower efficiency than charged BTZ black holes.
- Thermodynamics satisfies the Smarr formula with an additional parameter.

## Abstract

In this paper we have studied two non-linear black holes in 2+1 dimensions. They are regular and could have two horizons for chosen values of the parameters in the theory. Thermodynamics of the two black holes are studied in the extended phase space where the pressure P = -{\Lambda}/8{\pi}. In order to satisfy the Smarr formula and the first law of thermodynamics, a renormalization parameter is introduced. Hence there is an additional thermodynamical parameter for the black hole. We have also studied the two black holes in the context of heat engines. A thermodynamical cycle, consisting of two isobaric and two isochoric is considered. Efficiency is computed by varying the non-linear parameter and the electric charge of the black hole. It is observed that when the non-linear parameter and the charge increases, the efficiency increases. When compared to the charged BTZ black hole, the efficiency for the rectangle cycle is smaller for the regular black holes.