Can the fluctuations of a black hole be treated thermodynamically?

TL;DR

This paper demonstrates that black hole fluctuations are thermodynamically treatable because their fluctuations surpass quantum ones, and introduces an interpretation of fluctuation ratios as effective constituents of black holes.

Contribution

It clarifies that black hole thermodynamic fluctuations are significant and provides a novel interpretation linking fluctuation ratios to black hole constituents.

Findings

Thermodynamic fluctuations are larger than quantum fluctuations for black holes.

The ratio of fluctuations indicates the effective number of constituents in a black hole.

Black hole fluctuations can be meaningfully described using thermodynamic concepts.

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.