# Instability of Super-Entropic Black Holes in Extended Thermodynamics

## TL;DR

This paper investigates the thermodynamic instability of super-entropic black holes, showing that their negative specific heat indicates a fundamental instability, with implications for a broad class of such solutions.

## Contribution

It demonstrates that super-entropic black holes have negative specific heat, revealing a new fundamental instability and suggesting this may be a universal feature among them.

## Key findings

- Super-entropic black holes violate the reverse isoperimetric inequality.
- Their specific heat at constant volume is negative.
- Numerical evidence supports the instability across many solutions.

## Abstract

The charged black hole of Banados, Teitelbiom and Zanelli is studied in extended gravitational thermodynamics where there is a dynamical pressure and volume. It is a simple example of a super-entropic black hole, violating the reverse isoperimetric inequality. It is proven that this property implies that its specific heat at constant volume is negative, signalling a new kind of fundamental instability for black holes. It is conjectured that this instability is present for other super-entropic black holes, and this is demonstrated numerically for a large family of known solutions.