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.
Categories: hep-th gr-qc