Two black holes circle in a cosmic dance, spiraling closer together. In the end, they merge into one, and that moment unleashes a powerful burst of gravitational waves, ripples in spacetime itself. But what remains after the merger? A new black hole with a certain mass, spin rate, and an unexpected 'kick'—it can get a shove and fly off in a different direction.

Previously, to find out these properties, you had to either run long computer calculations or settle for rough estimates. Now, a team of researchers has created a universal 'calculator'—a set of formulas that deliver answers almost instantly. They fed the algorithms data from five thousand precise simulations (where black holes were modeled according to Einstein's laws) plus another thousand simpler calculations for pairs with a huge mass difference.

The result is two models: one for simple cases where black holes spin in the same plane, and another for more complex scenarios with tilted spin axes. The models weren't just fitted to the data; they used hints from established theories and even artificial intelligence for fine-tuning. The result beats all previous analogs in accuracy and rivals complex computer models, but computes in seconds. Now astronomers can quickly analyze signals from gravitational wave detectors and map the black hole population across the universe.