Universality for Black Hole Heat Engines Near Critical Points

TL;DR

This paper investigates how black hole heat engines near critical points can approach Carnot efficiency with finite power, analyzing the role of critical exponents and applying findings to various black hole classes.

Contribution

It extends previous work by characterizing the approach to Carnot efficiency near critical points and explores implications for Lovelock black holes with non-mean field critical exponents.

Findings

Efficiency approaches Carnot limit near critical points.

Critical exponents govern the rate of efficiency approach.

Odd-order Lovelock black holes with isolated critical points are consistent with thermodynamics.

Abstract

Johnson has shown [arXiv:1703.06119] that in the vicinity of a critical point the efficiency of a black hole heat engine can approach the Carnot efficiency while maintaining finite power. We characterize and extend this result in several ways, and we show how the rate of approach to the Carnot efficiency is governed by the critical exponents. We apply these results to several classes of black holes to illustrate their validity. Odd-order Lovelock black holes are known to have isolated critical points for which the critical exponents differ from the mean field theory values, providing a non-trivial test of the results. In this case, our results indicate the impossibility of even-order Lovelock black holes with isolated critical points in this class: their existence would constitute a violation of the second law of thermodynamics.