Microscopic black holes may form under conditions very different from those that create the massive black holes found at the centers of galaxies or produced by the collapse of giant stars. According to new research, these tiny black holes can emerge when spacetime reaches an unusual critical state and organizes into repeating, crystal-like patterns.
Researchers from Goethe University Frankfurt and the Vienna University of Technology have developed a mathematical explanation for this process. Using an unconventional approach, they derived a precise analytical formula describing how critical collapse can transform a spacetime crystal into a microscopic black hole.
Microscopic black holes and gravitational collapse
The black holes most commonly associated with astronomy are created by extreme cosmic events, such as the collapse of massive stars. However, physics does not impose a strict lower size limit on black holes. Under special critical conditions, even a tiny increase in energy can determine whether a system disperses or collapses into a black hole.
Similar conditions may have existed in the early universe shortly after the Big Bang, when matter and energy occupied an extremely dense and chaotic environment. If so, these conditions could have produced primordial black holes.
Computer simulations had previously shown that these unusual critical structures could exist. The remaining challenge was to develop a mathematical model capable of reproducing the simulation results. Researchers at Goethe University Frankfurt and the Vienna University of Technology addressed this challenge with a formula that can be calculated analytically, in principle using only paper and pencil.
How tiny changes can trigger gravitational collapse
“Sometimes small, seemingly insignificant causes are enough to produce huge and dramatic changes,” says Daniel Grumiller, a professor at the Vienna University of Technology. “Consider liquid water at 0 degrees Celsius. A very small change can cause the water to freeze. Its molecules then spontaneously arrange themselves into a regular structure, forming ice crystals.”
Einstein’s theory of general relativity suggests that spacetime can undergo similar transitions. Matter influences the geometry of spacetime, meaning that changes in the distribution of particles can alter its curvature.
“Mass curves spacetime,” explains Christian Ecker of the Institute for Theoretical Physics at Goethe University Frankfurt. “Large objects such as stars create strong curvature, which can be observed when light is deflected by a massive body. Smaller masses also curve spacetime, although their effects are weaker.”
Under critical conditions, spacetime curvature can form patterns that repeat across space and time. The researchers describe this structure as a type of “spacetime crystal.” The delicate transition that creates it is known as critical collapse.
“This spacetime crystal is a unique and fascinating object,” Grumiller says. “It represents an unstable intermediate state that can evolve in two different directions. It may dissolve, leaving ordinary spacetime filled with freely moving particles. However, if a tiny amount of energy is added, the system follows a different path: the seemingly ordinary spacetime crystal collapses and forms a black hole.”
Black hole formation predictions date back to 1993
Computer simulations first indicated in 1993 that black holes could form spontaneously through this type of critical behavior. For decades, physicists have attempted to describe the process mathematically, but deriving the required equations has remained highly challenging.
Researchers in Vienna and Frankfurt overcame this difficulty by changing the number of dimensions used in their calculations.
“Our universe has four dimensions: three dimensions of space and one dimension of time,” explains Christian Ecker. “In principle, however, there is nothing preventing us from formulating physical equations in more dimensions—five, 42, or even infinitely many.”
Although adding dimensions may seem likely to make a difficult problem even more complicated, the opposite can occur. Certain complex calculations become significantly easier as the number of dimensions approaches infinity.
Using infinite dimensions to solve four-dimensional physics
The researchers first studied the problem in a hypothetical space with an infinite number of dimensions. They then examined whether the resulting solutions could be translated back into lower-dimensional settings, including the four-dimensional spacetime of our universe.
This mathematical detour enabled the team to extract information about critical gravitational collapse that had previously been extremely difficult to calculate analytically.
“We found that our technique is surprisingly stable. Depending on the required level of accuracy, we can systematically improve the formula with additional approximation methods,” says Florian Ecker of the Vienna University of Technology. “This provides a new way to study black hole formation and other related phenomena that could not previously be analyzed analytically.”
The new method could give physicists a powerful tool for investigating microscopic black holes, critical collapse, and other extreme behaviors in spacetime without relying entirely on numerical computer simulations.
Source: www.sciencedaily.com