Can the fluctuations of a black hole be treated thermodynamically?

Abstract

Since the temperature of a typical Schwarzschild black hole is very low, some doubts are raised about whether the fluctuations of the black hole can be treated thermodynamically. It is shown that this is not the case: the thermodynamic fluctuations of a black hole are considerably larger than the corresponding quantum fluctuations. Moreover the ratio of the mean square thermodynamic fluctuation to the corresponding quantum fluctuation can be interpreted as a number of the effective constituents of a black hole.