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.
as written by the authors arXiv:2604.28050
Can a smooth horizon hide its microstates? At fixed classical and superselected data, the exterior distinguishability $$D_{\max}$$ of same-sector infalling states and the departure $$\varepsilon$$ from isometric infall obey $$D_{\max}^{2}+(1-2\varepsilon)^{2}\leq 1$$, and every point is realized. Below maximal disruption, the boundary is reached only by which-state measurements: the distinguished pair crosses undisturbed while the exterior records which one fell in. The least a horizon can do to have microstate hair is measure what falls in. Classically hairy black holes are labeled backgrounds, not microstate hair.
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.