Does Memory Burden Open a New Mass Window for Primordial Black Holes as Dark Matter?

It has been argued that the so-called memory-burden effect could cause black holes to become stabilized by the information that they carry, thereby suppressing the rate at which they undergo Hawking evaporation. It has furthermore been suggested that this opens a new mass window, between 10⁴\, g M 10¹⁰\, g, over which primordial black holes could constitute the dark matter of our Universe. We show in this letter that this is true only if the transition from the semi-classical phase of a black hole to its memory-burdened phase is practically instantaneous. If this transition is instead more continuous, Hawking evaporation will persist at relevant levels throughout the eras of Big Bang Nucleosynthesis and recombination, leading to stringent constraints which rule out the possibility that black holes lighter than ~ 4 × 10¹⁶\, g could make up all or most of the dark matter.