A black hole has three laws, just like an ideal gas. The first: energy is conserved. The second: the horizon area never decreases. And the third, the most finicky, demands that at zero temperature the entropy (a measure of disorder) tend to zero or a universal constant. The famous Bekenstein–Hawking formula ties entropy to the horizon area, but as a black hole cools, the area doesn't vanish, and the third law cracks at the seams.
The authors see this not as a death sentence but as a hint. The semiclassical approximation from which the formula is derived simply breaks down at very low temperatures. They construct a new expression for entropy that honestly goes to zero along with temperature, and in the hot limit returns to the familiar area law. The underlying image is a coin: a black hole has N microscopic bits, each of which can be 'heads' or 'tails', but with a slight bias toward mass. Entropy then measures how much this biased distribution differs from a perfectly symmetric one.
The real surprise is in the details. From the microscopic picture emerges a natural mass limit: a black hole cannot be heavier than M₀ = √N · $M_P$, where $M_P$ is the Planck mass (about 22 micrograms — the weight of an eyelash). This ceiling governs the very bias of the 'coin'. And the familiar horizon area turns out to be just the first, crudest term in an expansion in 1/N. The remaining terms are finite-information corrections that wash out in the classical limit.
The Planck mass is about 22 micrograms. That's the weight of a single eyelash, and yet in theory such tiny building blocks set the mass limit for an entire black hole.
The idea of a black hole mass limit echoes the 'ultimate collapse' in Greg Egan's novel Schild's Ladder, where physical constraints dictate the fate of entire civilizations.