Extremal black holes and the limits of the third law

Recent results of quantum field theory on a curved spacetime suggest that extremal black holes are not thermal objects and that the notion of zero temperature is ill-defined for them. If this is correct, one may have to go to a full semiclassical theory of gravity, including backreaction, in order to make sense of the third law of black hole thermodynamics. Alternatively it is possible that we shall have to drastically revise the status of extremality in black hole thermodynamics. Since the early 1970s, relativists have recognized that a remarkable analogy exists between the three laws of thermodynamics and the behavior of black holes, behavior that is encoded in the three laws of black hole dynamics. Indeed, since Hawking’s celebrated discovery of black hole radiation [1], the general consensus has been that the laws of black hole dynamics are no mere analogy, as remarkable as the analogy may be, but precisely the laws of thermodynamics applied to black holes. Historically, most research has focused on the first and second laws, which explicitly identify the surface area of a black hole with its entropy. In the past few years, however, increasing attention has been paid to the third law, and it may be the third law that is pointing toward the limits of black hole thermodynamics as currently understood. The third law of ordinary thermodynamics admits two different formulations, both due to Nernst. The “entropic” formulation states that the entropy of a system approaches a constant, independent of all the macroscopic parameters, as the temperature approaches absolute zero. According to the Planck postulate, this constant can be set equal to zero. The second formulation, the so-called “unattainability” law, states that it is impossible to reach absolute zero in a finite number of steps. For common physical systems the [email protected] [email protected] [email protected]