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A Mathematical ‘Spacetime Crystal’ Could Collapse Into a Tiny Black Hole

Physicists from Goethe University Frankfurt and TU Wien have derived an exact mathematical description of a theoretical spacetime structure that may either disperse or collapse into a microscopic black hole after a very small energy change.

A Mathematical ‘Spacetime Crystal’ Could Collapse Into a Tiny Black Hole

Daily Weird News Report

A theoretical structure resembling a crystal could mark the tipping point between ordinary spacetime and a microscopic black hole, according to research from Goethe University Frankfurt and TU Wien reported by ScienceDaily. The researchers describe the structure as a “spacetime crystal”: a temporary, repeating arrangement of spacetime’s curvature across space and time. It would exist in a finely balanced condition known as critical collapse, in which a slight change can send the system along one of two sharply different paths. With no significant additional energy, the structure could dissolve and leave behind ordinary spacetime containing freely moving particles. If a small amount of energy were added, however, the researchers’ model indicates that it could instead collapse into a black hole. The idea concerns black holes much smaller than the familiar objects associated with collapsing stars or the centers of galaxies. The source report notes that computer simulations had suggested since 1993 that black holes might form through this kind of critical behavior, but finding an exact mathematical description had remained difficult. The team’s solution used an unusual mathematical strategy. Rather than working directly only with the four dimensions of our universe—three dimensions of space and one of time—the researchers first examined the equations as the number of dimensions approached infinity. They then investigated how the resulting solution could be connected back to systems with fewer dimensions, including four-dimensional spacetime. According to the report, this approach made it possible to derive an analytical formula for the phenomenon and to improve the result systematically through additional approximation methods. The work was presented as a potential tool for studying black-hole formation and other extreme spacetime behavior without relying entirely on numerical computer simulations. The model also raises the possibility that similar conditions could have existed in the early universe, when matter and energy were packed into an intensely chaotic environment. The source material says such circumstances may have produced primordial black holes, but the reported work is a mathematical description of the proposed process rather than an observation of one occurring in nature.

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