# Critical Black Holes in a Large Charge Limit

## TL;DR

This paper explores the thermodynamic phase structure of charged black holes in anti-de Sitter space, focusing on critical phenomena and a novel large charge limit that simplifies the spacetime to a decoupled Rindler geometry.

## Contribution

It introduces a new large charge limit for black holes that reveals simplified thermodynamic behavior and connects to low-temperature thermodynamics and heat engine efficiency.

## Key findings

- Critical black hole properties at phase transition points analyzed.
- Large charge limit leads to a decoupled Rindler spacetime.
- Black hole thermodynamics linked to Carnot efficiency in this limit.

## Abstract

The extended thermodynamics of Reissner-Nordstr\"om charged black holes in D-dimensional anti-de Sitter spacetime has a phase structure in the (T,p) plane that includes a line of first order phase transitions ending in a second order transition point. For each D>=4, properties of the critical black hole at that point are explored, motivated by the observation that in D=4 its neighbourhood plays a core role in defining a very special class of heat engines that asymptote to Carnot efficiency in the large charge limit. This new limit provides a model of a novel low-temperature thermodynamic system. The double limit of approaching the horizon while sending q large at an appropriate rate yields a fully decoupled D-dimensional Rindler spacetime with zero cosmological constant.