When two heavy bodies collide, they don't always stay put. Merging black holes get a powerful kick, like the recoil of a gun, but instead of gunpowder, it's the curvature of spacetime doing the work. This kick can send the new hole flying out of a galaxy's center or even beyond its outskirts.

The authors analyzed data from the LIGO and Virgo gravitational-wave observatories spanning several years. They calculated recoil velocities for individual events and for the whole population. For two events, they got fairly precise estimates: the black hole GW231028-153006 shot off at about 839 km/s, and GW231123-135430 at about 974 km/s. That's hundreds of times faster than a bullet.

But for most events, the speeds remained uncertain: the data don't allow a precise determination of how strong the kick was. So the scientists went further and estimated the distribution of speeds for all merging black holes. It turns out the median recoil speed is roughly 300–330 km/s. That means half of all new holes fly off slower than this, and half faster.

Next, the authors calculated whether such holes would be retained by different types of star clusters and galaxies. In globular clusters, dense swarms of old stars, gravity is weak, so only 2–3% of merged holes are retained. In nuclear star clusters, which sit at the centers of galaxies, retention is higher—28–32%. Dwarf galaxies retain 25–29%, and giant ellipticals retain almost all: 92–94%.

But being retained doesn't mean returning to the center. A hole can linger at the cluster's edge for a long time, like a ball knocked out of the field but not over the fence. The authors calculated how long it takes for dynamical friction against stars to bring the hole back to the core. It turns out that in globular and nuclear clusters, this timescale can be very long — longer than the age of the Universe. So even a retained hole won't have time to find a partner for a new merger.

This changes the picture of how black holes grow. Previously, it was thought that if a hole stayed in a cluster, it would eventually merge again. Now it's clear: retaining is not enough — the hole also needs to make it back to the thick of things. In globular clusters, that's nearly impossible, so hierarchical mergers (where a hole merges, then its descendant merges again) are rare. But in massive elliptical galaxies, where gravity holds everything firmly in place, black holes can grow like a snowball.