Black hole dance illuminates hidden math of the universe

Scientists have made the most accurate predictions yet of the elusive space-time disturbances caused when two black holes fly closely past each other.

The new findings, published Wednesday (May 14) in the journal Nature, show that abstract mathematical concepts from theoretical physics have practical use in modeling space-time ripples, paving the way for more precise models to interpret observational data.

Gravitational waves are distortions in the fabric of space-time caused by the motion of massive objects like black holes or neutron stars. First predicted in Albert Einstein's theory of general relativity in 1915, they were directly detected for the first time a century later, in 2015. Since then, these waves have become a powerful observational tool for astronomers probing some of the universe's most violent and enigmatic events.

To make sense of the signals picked up by sensitive detectors like LIGO (the Laser Interferometer Gravitational-Wave Observatory) and Virgo, scientists need extremely accurate models of what those waves are expected to look like, similar in spirit to forecasting space weather. Until now, researchers have relied on powerful supercomputers to simulate black hole interactions that require refining black hole trajectories step by step, a process that is effective but slow and computationally expensive.

Now, a team led by Mathias Driesse of Humboldt University in Berlin has taken a different approach. Instead of studying mergers, the researchers focused on "scattering events" — instances in which two black holes swirl close to each other under their mutual gravitational pull and then continue on separate paths without merging. These encounters generate strong gravitational wave signals as the black holes accelerate past one another.

To model these events precisely, the team turned to quantum field theory, which is a branch of physics typically used to describe interactions between elementary particles. Starting with simple approximations and systematically layering complexity, the researchers calculated key outcomes of black hole flybys: how much they are deflected, how much energy is radiated as gravitational waves and how much the behemoths recoil after the interaction.

Their work incorporated five levels of complexity, reaching what physicists call the fifth post-Minkowskian order — the highest level of precision ever achieved in modeling these interactions.

Reaching this level "is unprecedented, and represents the most precise solution to Einstein's equations produced to date," Gustav Mogull, a particle physicist at Queen Mary University of London and a co-author of the study, told Space.com.

The team's reaction to achieving the landmark precision was "mostly just astonishment that we managed to get the job done," Mogull recalled.

While calculating the energy radiated as gravitational waves, researchers found that intricate six-dimensional shapes known as Calabi–Yau manifolds appeared in the equations. These abstract geometrical structures — often visualized as higher-dimensional analogues of donut-like surfaces — have long been a staple of string theory, a framework attempting to unify quantum mechanics with gravity. Until now, they were believed to be purely mathematical constructs, with no directly testable role tied to observable phenomena.

In the new study, however, these shapes appeared in calculations describing the energy radiated as gravitational waves when two black holes cruised past one another. This marks the first time they've appeared in a context that could, in principle, be tested through real-world experiments.

Mogull likens their emergence to switching from a magnifying glass to a microscope, revealing features and patterns previously undetectable. "The appearance of such structures sheds new light on the sorts of mathematical objects that nature is built from," he said.

These findings are expected to significantly enhance future theoretical models that aim to predict gravitational wave signatures. Such improvements will be crucial as next-generation gravitational wave detectors — including the planned Laser Interferometer Space Antenna (LISA) and the Einstein Telescope in Europe — come online in the years ahead.

"The improvement in precision is necessary in order to keep up with the higher precision anticipated from these detectors," Mogull said.