A black hole is not a frozen sphere. It's more like a soap bubble, whose walls can expand and contract. It even has two layers: the outer horizon, beyond which light cannot return, and the inner one, hidden deeper. When the hole swallows matter or loses energy, both layers shift, like the film of a bubble changing size.
Previously, when deriving the energy conservation law for a black hole (the analogue of the first law of thermodynamics), physicists artificially fixed the inner horizon. They multiplied Einstein's equations by the change in volume, but only for the outer boundary. This worked, but it was like trying to describe breathing while holding one nostril shut. The new approach lets both horizons move simultaneously. Instead of volume change, it uses the change in entropy — a measure of disorder, which for a black hole is tied to the horizon area. The field equations, written on each horizon, are multiplied by the corresponding entropy change, and everything combines into a single law without extra props.
The method turned out to be surprisingly robust. It works not only in Einsteinian gravity but also in theories with higher derivatives — more complex versions where spacetime curves in trickier ways. The authors also showed that for holes with three independent characteristics (mass, spin, charge), old schemes relying only on horizon radii break down. The correct path is to consider changes directly in the space of these three parameters, like coordinates on a map. Then the first law of thermodynamics emerges naturally, without additional constraints.
The area of a black hole's horizon never decreases: this is akin to the law of entropy non-decrease in ordinary physics. Stephen Hawking showed that holes can still lose mass through quantum radiation, but then entropy is carried away by the radiation, and the overall balance is maintained.
In Dan Simmons' novel 'Hyperion', the Time Tombs are surrounded by anti-entropic fields that move backward along the thermal arrow, like the inner horizon of a hole, living by its own rules.