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.