The Dark Dimension, the Swampland, and the Dark Matter Fraction Composed of Primordial Near-Extremal Black Holes

In a recent publication we studied the decay rate of primordial black holes perceiving the dark dimension, an innovative five-dimensional (5D) scenario that has a compact space with characteristic length-scale in the micron range. We demonstrated that the rate of Hawking radiation of 5D black holes slows down compared to 4D black holes of the same mass. Armed with our findings we showed that for a species scale of ${\cal O} (10^{9}~{\rm GeV})$, an all-dark-matter interpretation in terms of primordial black holes should be feasible for black hole masses in the range $10^{14} \lesssim M/{\rm g} \lesssim 10^{21}$. As a natural outgrowth of our recent study, herein we calculate the Hawking evaporation of near-extremal 5D black holes. Using generic entropy arguments we demonstrate that Hawking evaporation of higher-dimensional near-extremal black holes proceeds at a slower rate than the corresponding Schwarzschild black holes of the same mass. Assisted by this result we show that if there were 5D primordial near-extremal black holes in nature, then a PBH all-dark-matter interpretation would be possible in the mass range $10^{7}\sqrt{\beta} \lesssim M/{\rm g} \lesssim 10^{21}$, where $\beta$ is a parameter that controls the difference between mass and charge of the associated near-extremal black hole.