Physicists have described the invisible edge of a black hole

Researchers have now described such states using string theory. The key point is that the calculation turned out to be finite; in other words, it did not diverge to infinity, as is often the case in conventional quantum theories at very small distances.

The paper has been published in *Physical Review Letters*.

Details

In physics, a horizon is a boundary. The best-known example is the event horizon of a black hole. There are other horizons too, for example in models of an expanding universe.

When physicists divide space into two regions — an accessible region and an inaccessible region — additional quantum states may appear at the boundary. These are called edge modes. Put simply, these are states that do not exist ‘deep within’ space, but rather near its edge.

Such states are important because they may be linked to the entropy of the event horizon. And the entropy of black holes is one of the major questions in modern physics: if a black hole has temperature and entropy, then there must be some microscopic states underlying them.

What was the problem?

In standard quantum field theory, calculations near the event horizon often yield infinities. This happens because the theory allows for an infinite number of minute fluctuations right at the boundary.

String theory works differently. In it, particles are not treated as points, but as tiny ‘strings’. Thanks to this, at extremely small distances the theory behaves more smoothly and can avoid certain mathematical infinities.

The authors of the paper — Atish Dabholkar, Eleanor Harris and Upamanyu Moitra — investigated whether it is possible to describe the boundary conditions of the horizon in such a way that the result is compatible with string theory and remains finite. In their published paper, they demonstrated that, after summing the contributions from all string fields, the result is a modularly invariant and ultraviolet-finite distribution function.

In simple terms

Conventional theory seems to suggest that at the edge of the horizon there are an infinite number of tiny quantum ‘flickerings’, and the mathematics cannot cope.

String theory offers a different perspective: at the very smallest scales, the world does not consist of point particles. Therefore, space cannot be divided into an infinite number of parts. In the new calculation, this helped to describe states near the horizon without a mathematical explosion.

In a nutshell: physicists have found a way to calculate the quantum ‘edge’ of the horizon so that the result is finite.

Why this is important

Black holes have long baffled physicists. According to general relativity, they are objects from which nothing can escape. But quantum physics suggests that subtle processes involving information, temperature and entropy must be taking place at the event horizon.

The new work does not resolve all these issues. However, it provides a more precise framework for describing quantum states at the event horizon. The paper explicitly states that the result can be interpreted in terms of counting states, which is important for understanding the microscopic nature of the entropy of event horizons.

Put simply, this is a step towards answering the question: what does quantum information ‘consist of’ at the edge of a black hole?

Background

The black hole horizon is not a solid surface. It is a boundary in space-time: once you cross it, there is no way back out.

But in quantum physics, boundaries often turn out not to be empty. Additional states can appear on them. Such ideas are found not only in black hole physics, but also in other fields, such as systems with quantum edge effects.

This is precisely why it is important for physicists to understand how such states are organised at the horizons. If they can be calculated correctly, this could bring science closer to a more complete connection between quantum mechanics and gravity.

Source

Research: Atish Dabholkar, Eleanor Harris, Upamanyu Moitra — “Edge Modes on Stringy Horizons”, Physical Review Letters, 2026.