\(f(R)\) black holes as heat engines. (English) Zbl 1373.83074
Summary: With the cosmological constant considered as a thermodynamic variable in the extended phase space, it is natural to study the thermodynamic cycles of the black hole, which is conjectured to be performed using renormalization group flow. We first investigate the thermodynamic cycles of a 4-dimensional asymptotically AdS \(f(R)\) black hole. Then we study the thermodynamic cycles of higher dimensional asymptotically AdS \(f(R)\) black holes. It is found that when \(\Delta V \ll \Delta P\), the efficiency of isobar-isochore cycles running between high temperature \(T_H\) and low temperature \(T_C\) will increase to its maximum value, which is exactly the Carnot cycles’ efficiency both in 4-dimensional and in higher dimensional cases. We speculate that this property is universal for AdS black holes, if there is no phase transition in the thermodynamic cycle. This result may deepen our understanding of the thermodynamics of the AdS black holes.
MSC:
83C57 | Black holes |
80A10 | Classical and relativistic thermodynamics |
83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |
81T17 | Renormalization group methods applied to problems in quantum field theory |
83E15 | Kaluza-Klein and other higher-dimensional theories |
Keywords:
\(f(R)\) black hole; heat engine; Carnot cycle; extended phase space; renormalization group flowReferences:
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