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.
as written by the authors arXiv:2608.05795v1
Although the Bekenstein-Hawking area law is consistent with the first and second laws of black hole thermodynamics, it appears to be in conflict with the third law, which in the Nernst formulation states that the entropy should either vanish or approach a universal constant in the zero-temperature limit. We argue that this tension reflects a limitation of the semiclassical area law rather than a fundamental feature of black hole thermodynamics. On this basis, we obtain an entropy formula that is consistent with the third law, and approaches Bekenstein-Hawking entropy in the high-temperature limit. The resulting entropy admits a simple microscopic interpretation, and it can be written as the Kullback-Leibler divergence between a mass-biased Bernoulli distribution and the uniform distribution on N microscopic bits. From this perspective, the thermodynamic black hole entropy admits an information-theoretic representation as an entropy deficit, namely as the relative entropy between the black hole ensemble and a maximally mixed reference ensemble. The Bekenstein-Hawking area law then emerges as the leading term in an $$1/N$$ expansion, while a universal mass scale $$M_0=\sqrt{N}\,M_P$$, interpreted as an absolute upper bound on the black hole mass, controls the bias of the underlying microscopic ensemble. The subleading terms represent finite-information corrections to the classical area law.
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.