Thermodynamic optimization of a Penrose process: an engineers' approach to black hole thermodynamics

Abstract

In this work we present a new view on the thermodynamics of black holes introducing effects of irreversibility by employing thermodynamic optimization and finite-time thermodynamics. These questions are of importance both in physics and in engineering, combining standard thermodynamics with optimal control theory in order to find optimal protocols and bounds for realistic processes without assuming anything about the microphysics involved. We find general bounds on the maximum work and the efficiency of thermodynamic processes involving black holes that can be derived exclusively from the knowledge of thermodynamic relations at equilibrium. Since these new bounds consider the finite duration of the processes, they are more realistic and stringent than their reversible counterparts. To illustrate our arguments, we consider in detail the thermodynamic optimization of a Penrose process, i.e. the problem of finding the least dissipative process extracting all the angular momentum from a Kerr black hole in finite time. We discuss the relevance of our results for real astrophysical phenomena, for the comparison with laboratory black holes analogues and for other theoretical aspects of black hole thermodynamics.