Researchers from Goethe University Frankfurt and TU Wien have developed a mathematical framework for describing the formation of microscopic black holes through a process involving the organization of spacetime into a repeating, crystal-like structure. While computer simulations had previously indicated this phenomenon was possible, deriving an analytical formula proved exceptionally challenging until now.
According to the researchers, black holes theoretically have no strict lower size limit. Microscopic versions could arise under special critical conditions where even minimal energy additions determine whether a system disperses or collapses. Such circumstances may have existed in the early universe following the Big Bang, potentially producing primordial black holes. The process resembles phase transitions observed in ordinary matter—when spacetime’s curvature arranges itself into a repeating pattern under critical conditions, the resulting structure is termed a “spacetime crystal.”
This spacetime crystal represents an unstable intermediate state capable of evolving in two directions. It may dissolve into ordinary spacetime containing freely moving particles, or if a small amount of energy is added, it can undergo complete transformation into a black hole. Computer simulations first suggested this critical collapse mechanism in 1993, but physicists spent decades attempting to reproduce the process with mathematical equations.
The Vienna and Frankfurt teams circumvented the problem by changing the dimensional framework of their calculations. Rather than working in the four dimensions of actual spacetime, they analyzed the physics in hypothetical spaces with many more dimensions. Counterintuitively, certain complex calculations become more tractable as dimensionality increases toward infinity. After solving the problem in this extended dimensional space, researchers investigated whether the solution could be translated back to four-dimensional spacetime.
This mathematical approach provided new analytical tools for studying black hole formation and extreme spacetime behaviors. The technique demonstrates remarkable stability, allowing systematic improvement of formulas through additional approximation methods. The methodology could offer physicists an alternative to relying entirely on numerical computer simulations for investigating black-hole-related phenomena.
Article Attribution | Read More at Article Source
Article summary produced by Claude AI