Scientists from Goethe University Frankfurt and TU Wien have developed a mathematical framework for describing how microscopic black holes could emerge from unusual critical states in spacetime. While most familiar black holes result from catastrophic cosmic events like stellar collapse, physics permits the existence of much smaller black holes under specific conditions where minimal energy additions determine whether a system disperses or collapses.
The researchers drew inspiration from phase transitions in ordinary matter, such as water freezing at zero degrees Celsius. Under analogous critical conditions, spacetime itself can organize into a repeating, crystalline pattern influenced by the distribution of matter and energy. This structure, termed a “spacetime crystal,” represents an unstable intermediate state that can either dissolve back into ordinary spacetime or, if energy is added, transform into a black hole. Such phenomena may have occurred in the early universe following the Big Bang, potentially producing primordial black holes.
Computer simulations demonstrated the feasibility of critical collapse beginning in 1993, but translating these computational results into exact mathematical formulas proved extraordinarily challenging. The Vienna and Frankfurt team overcame this obstacle using an unconventional approach: they analyzed the problem in hypothetical spaces with vastly larger numbers of dimensions than our four-dimensional universe. By working in higher-dimensional spaces, certain complex calculations become significantly simpler, allowing researchers to derive solutions analytically that can then be translated back to four-dimensional spacetime.
The resulting mathematical technique offers improved stability and precision through systematic approximation methods, according to the researchers. This approach provides physicists with new analytical tools for studying black hole formation and extreme spacetime behavior without depending entirely on numerical computer simulations, potentially opening new avenues for understanding fundamental physics.
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