Black Holes with Memory: Forgetfulness as the Engine of Dark Matter express
Black holes lose mass like water from a bucket in the sun — an evaporation discovered by Stephen Hawking. But tiny primordial black holes, born right after the Big Bang, behave differently: once they lose half their mass, a memory effect kicks in — as if the bucket covers itself with a lid. Jacob Bekenstein calculated this measure of disorder, entropy, for black holes.
Previously, it was thought the lid snaps shut instantly. Now physicists have modeled a smooth transition: the evaporation rates can add up or multiply. Comparing with data on the birth of light elements in the first minutes after the Big Bang showed that with addition, up to 10% of holes survive and could make up dark matter. With multiplication, only 1%.
A detail that changes the picture: a tiny black hole with the mass of a mountain and the size of a proton can survive to this day solely thanks to this memory. The slightest nuance in 'forgetfulness' determines whether it's the invisible foundation of the universe.
Original abstract
as written by the authors arXiv:2606.04707
Light primordial black holes (PBHs) are disfavored as dark matter if they evaporate through standard Hawking radiation alone. The memory-burden effect can extend their lifetimes by suppressing emission after roughly half the mass is lost. Existing cosmological studies often model the onset of this phase as an instantaneous transition between semi-classical and burden-dominated evaporation. We instead treat the crossover as continuous and compare additive versus multiplicative combinations of the two rates, using a smoothed tanh profile with parameters $$(q,\delta)$$. Monochromatic PBHs are mapped to a decaying scalar field and evolved with Modified AlterBBN during Big Bang nucleosynthesis (BBN). The two prescriptions yield distinct exclusion curves: the additive crossover always gives weaker bounds than the multiplicative one, while both are tighter than the instantaneous transition. For $$10^{5}\,\mathrm{g}\lesssim M_i\lesssim 10^{10}\,\mathrm{g}$$, the additive case can permit $$f_{\mathrm{PBH},0}\sim 10^{-1}$$ where the multiplicative case gives $$f_{\mathrm{PBH},0}\lesssim 10^{-2}$$. Specifying the rate-combination rule is therefore essential when translating memory-burden models into BBN constraints on PBH dark matter.
The smallest primordial black hole could weigh as much as a mountain, yet be the size of a proton, and it's still alive today thanks to the memory effect.