Determine late-time behavior of PBH evaporation in the memory burden regime

Determine the late-time evaporation behavior of non-spinning, uncharged four-dimensional primordial black holes after the semiclassical approximation breaks down due to the memory burden effect, specifically ascertaining whether the black hole temperature remains fixed at the half-decay value or continues to increase according to T(M) ∝ 1/M, and characterize the corresponding emission-rate evolution, lifetime, and potential explosive outcomes under each scenario.

Background

The paper models Hawking evaporation with a transition at half-decay to a regime where emission is suppressed by a factor depending on the black hole entropy, motivated by the memory burden effect. The authors implement a scenario with fixed temperature after half-decay and mention an alternative in which the temperature continues to rise with decreasing mass, potentially leading to a black hole explosion.

They explicitly state that the late-time behavior beyond the semiclassical regime is not known in sufficient detail and therefore restrict their analysis to the fixed-temperature scenario. Determining the correct late-time dynamics is essential for robust constraints on the primordial black hole dark matter fraction.