Critical heat engines in massive gravity

Abstract

Abstract With in the extended thermodynamics, we study the efficiency η 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, η 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: η −1 < η 0 < η +1. Furthermore, the study of the near horizon region of the critical hole shows that, apart from the known q → ∞ 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.