Physicists have mathematically described, for the first time, a quirk of spacetime geometry at the brink of black hole formation. The curvature of spacetime can organize into a highly ordered repeating state, reminiscent of time crystals. With a small energy addition, these structures can collapse into microscopic black holes.
Spacetime Crystal: A Fractal Dance at the Edge of Infinity
In 1993, physicist Matthew Choptuik discovered through computer simulations that the critical state at the threshold of black hole formation exhibits discrete self-similarity: repeating patterns across smaller scales. This state is known as a spacetime crystal.
"Sometimes a tiny, seemingly insignificant cause is enough to trigger a huge and dramatic change," said physicist Daniel Grumiller of the Technical University of Vienna. "Take liquid water at zero degrees Celsius, for example. A very small change is enough to make the water freeze. The water molecules then spontaneously arrange themselves into a regular pattern and form an ice crystal."
A New Analytical Window into Gravity
Researchers from the Technical University of Vienna and Goethe University Frankfurt approached the problem by considering general relativity in a large number of dimensions. By modeling universes with hundreds of dimensions, they derived analytical formulas describing the repeating, fractal-like structures in spacetime curvature during black hole collapse. The same mathematical structures persisted at lower dimensions, suggesting fundamental properties of gravity.
"Our technique turns out to be remarkably stable. Depending on the desired precision, we can systematically improve our formulas using additional approximation methods," said physicist Florian Ecker. "This gives us a new method for studying black-hole-related phenomena that could previously not be analyzed analytically."
The findings were published in Physical Review Letters.