Johnson [Phys. Rev. D 98, 026008 (2018)] has shown 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 nontrivial 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.

• Received 5 December 2022
• Accepted 3 January 2023

DOI:https://doi.org/10.1103/PhysRevD.107.044001