A comment on fluctuations and stability limits with application to superheated black holes

TL;DR

This paper clarifies the relationship between thermodynamic fluctuations and stability limits in black holes, demonstrating that black holes in large cavities remain stable and do not evaporate below the Hawking temperature despite high radiation entropy.

Contribution

It provides a clear link between fluctuations and stability, applying fluctuation theory to black holes in cavities, and challenges previous interpretations based solely on heat capacity signs.

Findings

Black holes in cavities larger than 10^6 Planck length are stable near the Hawking temperature.

Thermodynamic fluctuations directly indicate instability onset, not just heat capacity signs.

Black holes do not evaporate below the critical Hawking temperature in quasi-equilibrium states.

Abstract

We point out that, contrary to signs of heat capacities, thermodynamic fluctuations are simply and unequivocally related to onset of instabilities that show up near critical points. Fluctuation theory is then applied to \Schw\ \bh s surrounded by radiation. This shows that slowly evolving \bh s along quasi-equilibrium states in cavities greater than $10^6$ Planck length will not evaporate below the critical Hawking limit temperature despite the fact that pure radiation has a much higher entropy. (CQG in press, figure request to okamoto@gprx.miz.nao.ac.jp)