Drop a handful of sand into calm water — the ripples spread and fade. Drop it into a running blender — the vortices mix everything in an instant. Physics has a similar rule: chaos cannot grow faster than a certain rate. This limit, like a speed bump, was long considered unbreakable for many systems, from quantum particles to black holes.
But in recent years, astrophysicists have noticed something odd: around some black holes, chaos accelerates faster than allowed. In a new study, scientists tested dozens of black hole varieties — from simple ones described by Einstein to exotic ones with extra fields. And they found a common cause for the violations. It all comes down to where the last circular orbit lies, the one on which light can still circle without falling in (called the photon sphere).
When a black hole spins at nearly maximum speed, its horizon, the point of no return, and the photon sphere can almost coincide. Then time at the horizon flows infinitely slowly compared to a distant observer. This slowdown dampens any instabilities, and chaos obediently stays within the limit. But if the photon sphere hangs noticeably above the horizon, there's no slowdown, and chaos breaks loose.
The authors offer a simple rule: just look at the geometry, where the photon sphere sits relative to the horizon, and you can immediately tell whether the limit will be violated. This isn't just a mathematical trick; it hints at a deep connection between quantum chaos and the fabric of spacetime. Perhaps nature itself forbids chaos from being too fast where time stands still.
For a non-rotating black hole, the photon sphere sits at a distance of one and a half times the horizon radius. That's like the last safe circular lane for a cyclist being not at the cliff's edge, but a meter and a half away, and still doomed.
In Stanislaw Lem's novel 'Solaris', the planet's ocean creates structures that defy the usual laws of physics — a fitting nod to black holes, where chaos breaks the established bounds.