Islands of regularity emerge in the complex three-body problem

Islands of regularity emerge in the complex three-body problem
by Robert Schreiber
Berlin, Germany (SPX) Oct 11, 2024

When three massive objects encounter one another in space, their gravitational interactions are typically unpredictable and chaotic. However, a new discovery from a University of Copenhagen researcher suggests that these encounters can sometimes follow regular patterns, defying the conventional understanding of chaos. This finding could significantly enhance our knowledge of gravitational waves and other fundamental cosmic phenomena.

The popular Netflix series '3-Body Problem' draws attention to the complexities of such interactions. Inspired by Liu Cixin's novel, the series revolves around a star system with three gravitationally connected stars, highlighting the scientific puzzle that has intrigued researchers since Isaac Newton's time. While two-object interactions are predictable, the introduction of a third object creates chaotic behavior.

"The Three-Body Problem is one of the most famous unsolvable problems in mathematics and theoretical physics," explained Alessandro Alberto Trani of the University of Copenhagen's Niels Bohr Institute. "Our millions of simulations show that there are 'isles of regularity' in this chaos, which depend on the initial positioning, speed, and angle of the objects when they meet."

This discovery could lead to more accurate astrophysical models, especially as the three-body problem occurs frequently in the universe. A better understanding of these encounters is essential for studying gravitational waves and other phenomena involving massive objects like black holes.

"If we want to understand gravitational waves, the interactions of black holes as they meet and merge are crucial. These forces are immense, and our findings could be key to unlocking many of the universe's mysteries," said Trani.

Using his custom-built software, Tsunami, Trani conducted millions of simulations to analyze three-body encounters. These simulations, based on known physical laws such as Newton's gravity and Einstein's general relativity, revealed predictable patterns where chaos had previously been expected. The object with the lowest mass is usually ejected from the system, and the simulation results visually illustrate these regularities.

"If the problem were purely chaotic, we'd see a random mix of outcomes. But regular 'isles' emerge from the chaos, showing where the system behaves predictably," Trani elaborated.

This new understanding, however, presents a challenge for researchers. While pure chaos can be calculated statistically, introducing regularity complicates those calculations. Trani acknowledged that this discovery sets researchers "back to square one" in terms of understanding, but also opens the door to new insights in the long term.

Research Report:Isles of regularity in a sea of chaos amid the gravitational three-body problem