The announcement that the Laser Interferometer Gravitational-wave Observatory (LIGO) had detected gravitational waves during the merger of two black holes sent ripples throughout the scientific community in 2016. The earthshaking news not only confirmed one of Albert Einstein’s key predictions in his general theory of relativity, but also opened a door to a better understanding of the motion of black holes and other spacetime-warping phenomena.

Cataclysmic events such as the collision of black holes or neutron stars produce the largest gravitational waves. Binary black holes orbit around each other for billions of years before eventually colliding to form a single massive black hole. During the final moments as they merge, their mass is converted to a gigantic burst of energy — per Einstein’s equation e=mc2 — which can then be detected in the form of gravitational waves.

To understand the motion of binary black holes, researchers have traditionally simplified Einstein’s field equations and solved them to calculate the emitted gravitational waves. The approach is complex and requires expensive, time-consuming simulations on supercomputers or approximation techniques that can lead to errors or break down when applied to more complicated black hole systems.