Benchmarking Black Hole Heat Engines, II

TL;DR

This paper extends a benchmarking scheme to non-static black holes, specifically Kerr black holes, to compare their heat engine efficiencies using a circular cycle in the p-V plane, providing a new upper bound in certain limits.

Contribution

It introduces a benchmarking method for rotating black hole heat engines and derives an exact efficiency formula in an ideal-gas-like limit, enabling comparisons across different black hole types.

Findings

Derived an exact efficiency formula for Kerr black holes in a specific limit.

Compared efficiencies of Kerr black holes with static charged black holes.

Established an upper bound for rotating black hole heat engine efficiency.

Abstract

We extend to non-static black holes our benchmarking scheme that allows for cross-comparison of the efficiencies of asymptotically AdS black holes used as working substances in heat engines. We use a circular cycle in the p-V plane as the benchmark cycle. We study Kerr black holes in four spacetime dimensions as an example. As in the static case, we find an exact formula for the benchmark efficiency in an ideal-gas-like limit, which may serve as an upper bound for rotating black hole heat engines in a thermodynamic ensemble with fixed angular velocity. We use the benchmarking scheme to compare Kerr to static black holes charged under Maxwell and Born-Infeld sectors.