Physicists have recorded an anomalous state of space-time for the first time

Physicists have for the first time mathematically described an unusual state of spacetime that arises on the threshold of black hole formation. It turned out that at this moment, the curvature of spacetime can arrange itself into repeating structures resembling so-called time crystals. The work has been published in the journal Physical Review Letters (PRL).

During black hole formation, gravity becomes so extreme that the standard equations of Einstein's general theory of relativity are practically impossible to solve analytically. For this reason, scientists have studied this process for decades primarily through computer simulations.

A particularly challenging area is the so-called critical collapse — a state at the very boundary between two outcomes: matter either disperses back into space or ultimately collapses into a black hole.

Back in 1993, physicist Matthew Choptuik discovered that at this threshold, spacetime begins to exhibit "discrete self-similarity" — repeating structures that emerge at increasingly smaller scales. However, until now, no one had been able to describe this effect using rigorous mathematical formulas. Now researchers from the Vienna University of Technology and Goethe University Frankfurt have found a way to do so.

"This spacetime crystal is an extremely unusual and fascinating object," said physicist Daniel Grumiller.

According to the scientists, such structures behave like an unstable intermediate state. If just a small amount of energy is added, they can suddenly transition into a microscopic black hole state.

The key to the solution was an unusual mathematical idea: the scientists represented the Universe not as four-dimensional, but as multidimensional — with dozens or even hundreds of spatial dimensions.

"Nothing prevents us from writing physical equations for five, forty-two, or even an infinite number of dimensions," explained physicist Christian Ecker.

Surprisingly, in the multidimensional model, Einstein's equations become simpler: gravity concentrates locally near the region of collapse rather than being distributed across all of space. Using this approach, the researchers were able to derive analytical formulas describing the fractal repeating structures of spacetime curvature during black hole formation.

Moreover, similar mathematical patterns were preserved even when returning to fewer dimensions, which may indicate the fundamental nature of this phenomenon.

The authors believe that the new method will help study processes related to black holes that previously could only be investigated numerically on supercomputers.