Is there a black hole minimum mass?

TL;DR

This paper derives a thermodynamic lower bound on black hole mass, suggesting the existence of a minimum mass for classical black holes, which is close to the Planck mass, with implications for primordial black holes and early universe conditions.

Contribution

It introduces a thermodynamic derivation of a minimum black hole mass, linking entropy bounds to classical black hole formation limits.

Findings

Minimum black hole mass is approximately 0.04 times the square root of effective degrees of freedom times the Planck mass.

The minimum mass aligns with the lower bound for classical black hole formation against Hawking evaporation.

For primordial black holes, the minimum mass cannot be much greater than the Planck mass across different epochs.

Abstract

Applying the first and generalised second laws of thermodynamics for a realistic process of near critical black hole formation, we derive an entropy bound, which is identical to Bekenstein's one for radiation. Relying upon this bound, we derive an absolute minimum mass $\sim0.04 \sqrt{g_{*}}m_{\rm Pl}$, where $g_{*}$ and $m_{\rm Pl}$ is the effective degrees of freedom for the initial temparature and the Planck mass, respectively. Since this minimum mass coincides with the lower bound on masses of which black holes can be regarded as classical against the Hawking evaporation, the thermodynamical argument will not prohibit the formation of the smallest classical black hole. For more general situations, we derive a minimum mass, which may depend on the initial value for entropy per particle. For primordial black holes, however, we show that this minimum mass can not be much greater than the Planck mass at any formation epoch of the Universe, as long as $g_{*}$ is within a reasonable range. We also derive a size-independent upper bound on the entropy density of a stiff fluid in terms of the energy density.