Is there an upper bound on the size of a black-hole?

TL;DR

This paper explores the theoretical upper limit on black-hole size based on thermodynamic principles, suggesting a finite maximum horizon radius comparable to the Hubble horizon, with implications for cosmology.

Contribution

It introduces a thermodynamic argument for an upper bound on black-hole size, linking black-hole physics with cosmological scales.

Findings

Black-holes have a finite lower temperature due to statistical fluctuations.

An estimated upper bound on black-hole horizon radius is comparable to the Hubble horizon.

The bound has implications for understanding black-hole growth limits and cosmology.

Abstract

According to the third law of Thermodynamics, it takes an infinite number of steps for any object, including black-holes, to reach zero temperature. For any physical system, the process of cooling to absolute zero corresponds to erasing information or generating pure states. In contrast with the ordinary matter, the black-hole temperature can be lowered only by adding matter-energy into it. However, it is impossible to remove the statistical fluctuations of the infalling matter-energy. The fluctuations lead to the fact the black-holes have a finite lower temperature and, hence, an upper bound on the horizon radius. We make an estimate of the upper bound for the horizon radius which is curiosly comparable to Hubble horizon. We compare this bound with known results and discuss its implications.