BTZ black holes in massive gravity

TL;DR

This paper explores the properties of BTZ black holes in massive gravity, focusing on their thermodynamics, quantum effects, and efficiency as heat engines, revealing unique features like super-entropic behavior and Van der Waals phase transitions.

Contribution

It introduces a new BTZ black hole solution in massive gravity using Vainshtein and dRGT mechanisms, analyzing its thermodynamics and stability properties.

Findings

Black hole is super-entropic, violating the Reverse Isoperimetric Inequality.

Exhibits Van der Waals-like critical behavior.

Shows no quantum effects and displays thermal instabilities.

Abstract

We analyze certain aspects of BTZ black holes in massive theory of gravity. The black hole solution is obtained by using the Vainshtein and dRGT mechanism, which is asymptotically AdS with an electric charge. We study the Hawking radiation using the tunneling formalism as well as analyze the black hole chemistry for such system. Subsequently, we use the thermodynamic pressure-volume diagram to explore the efficiency of the Carnot heat engine for this system. Some of the important features arising from our solution include the non-existence of quantum effects, critical Van der Walls behaviour, thermal fluctuations and instabilities. Moreover, our solution violates the Reverse Isoperimetric Inequality and, thus, the black hole is super-entropic, perhaps which turns out to be the most interesting characteristics of the BTZ black hole in massive gravity.