A stone falls into a pond, and the ripples on the water tell for a long time where it sank. With a black hole, it would seem, things are different: everything that crosses the horizon (the boundary from beneath which not even light can escape) vanishes without a trace. Classical physics maintained that only mass, charge, and rotation are visible from outside — three 'bald' parameters. But quantum mechanics disagrees.
The authors built a simple model: two states of infalling matter (for example, two particles in different quantum states) and an external observer who tries to distinguish them after the fall. It turns out there is a hard constraint. The sum of the square of the distinguishability from outside and the square of the preservation of the infalling state cannot exceed 1. If the fall barely disturbs the particle (preservation close to 1), then the distinguishability from outside tends to zero — the horizon leaves no traces. But as soon as the slightest perturbation appears, the outside world gains the ability to tell what exactly fell in.
This is not just an abstract theorem. It means that any black hole has 'hair'—quantum microscopic states that inevitably manifest on the horizon. Classical 'hairy' solutions with additional fields are merely a backdrop, a decoration. The real hair is the indelible imprint of everything that has ever crossed the horizon. And so information is not lost without a trace: it remains at the boundary, like ripples on water.
The black hole information loss paradox tormented Stephen Hawking for three decades. In 2004, he publicly conceded defeat and paid off a lost bet — an encyclopedia of baseball, from which information can be extracted at any moment.
In the film 'Interstellar,' data from the black hole Gargantua is transmitted via gravitational anomalies — essentially a fictional illustration of 'hair' on the horizon, accessible to an external observer.