Critical Heat Engines in Massive Gravity

TL;DR

This paper investigates the efficiency of critical heat engines in charged black holes within massive gravity, revealing topology-dependent efficiency orderings and conditions for decoupled Rindler spacetime in the near horizon region.

Contribution

It demonstrates that the efficiency order of critical heat engines can be reversed based on topology and identifies new parameter scalings needed for decoupled Rindler spacetime.

Findings

Efficiency order can be reversed based on topology.

Additional scalings of parameters are required for Rindler spacetime.

Efficiency can be higher for spherical topology in critical heat engines.

Abstract

With in the extended thermodynamics, we study the efficiency $\eta_k$ of critical heat engines for charged black holes in massive gravity for spherical ($k=1$), flat ($k=0$) and hyperbolic ($k=-1$) topologies. Although, $\eta_k$ is in general higher (lower) for hyperbolic (spherical) topology, we show that this order can be reversed in critical heat engines with efficiency higher for spherical topology, following in particular the order: $ \eta_{\rm -1}^{\phantom{-1}} < \eta_{\rm 0}^{\phantom{0}} < \eta_{\rm +1}^{\phantom{+1}}$. Furthermore, the study of the near horizon region of the critical hole shows that, apart from the known $q\rightarrow \infty $ condition, additional scalings of massive gravity parameters, based on the topology of the geometry are required, to reveal the presence of a fully decoupled Rindler space-time with vanishing cosmological constant.