Physicists Derive Exact Formula for How a 'Spacetime Crystal' Becomes a Black Hole

Physicists at Goethe University Frankfurt and TU Wien in Vienna have derived, for the first time, an exact mathematical formula describing how spacetime can organize itself into a repeating, crystal-like pattern and then suddenly collapse into a microscopic black hole.

The researchers compared the process, called critical collapse, to water freezing into ice. "Sometimes a tiny, seemingly insignificant cause is enough to trigger a huge and dramatic change," said Prof. Daniel Grumiller of TU Wien. Just as a small drop in temperature makes water molecules snap into a regular ice crystal, matter can curve spacetime under the right conditions into a finely balanced, repeating pattern the researchers call a "spacetime crystal."

This state is unstable: it can either dissolve back into ordinary spacetime, or, if a tiny amount of energy is added, collapse into a black hole. Conditions like these may have existed shortly after the Big Bang, when matter and energy were packed into an intensely chaotic environment, potentially producing what physicists call primordial black holes.

Computer simulations first suggested in 1993 that black holes could form this way, but physicists could not derive the underlying equations analytically for decades. The Frankfurt and Vienna team solved the problem by working the calculations in a hypothetical space with far more dimensions than our universe's four, where the mathematics becomes simpler, and then translating the solution back down to four dimensions.

Florian Ecker of TU Wien said the method is "remarkably stable" and can be refined further with additional approximation techniques. The approach gives physicists a new way to study black hole formation and other extreme behaviour of spacetime without relying entirely on computer simulations.