Thermalization and hotspot formation around small primordial black holes

TL;DR

This paper investigates the temperature distribution around small primordial black holes, revealing a plateau in the plasma temperature and showing that naive models overestimate the temperature far from the black hole due to rapid particle escape.

Contribution

It provides an analytical and numerical analysis demonstrating the non-monotonic temperature profile around small black holes and the failure of local thermal equilibrium near the horizon.

Findings

Temperature profile features a plateau near the black hole

Background temperature far from the black hole is suppressed

Hawking radiation particles escape before thermalizing

Abstract

We quantitatively analyze a basic question: what is the stationary solution of the background plasma temperature profile around a black hole (BH)? One may naively expect that the temperature profile continuously decreases from the Hawking temperature at the surface of the BH towards an outer region. We show analytically and numerically that this is not the case because local thermal equilibrium cannot be maintained near the surface of the BH and also because the high-energy particles emitted from Hawking radiation cannot be instantaneously thermalized into the background plasma. The temperature profile has a plateau within a finite distance from the BH, and even the overall amplitude of background temperature at a distance far away from the BH is significantly suppressed compared with the naive expectation. The main reason for these counterintuitive results comes from the fact that the size of the BH is too small that particles of Hawking radiation goes far away within the typical time scale of interactions.