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Scrambling in a classical "black hole"

Nov 30 2015

In 1974, Hawking put forward the notion that black holes are not truly ‘black’. Instead, a black hole continuously burns and emits all of its mass in the form of thermal radiation. In recent years progress has been made in understanding this burning process. It turns out that black holes are highly efficient furnaces: when a bit of information is thrown into a black hole (say in the form of a particle), the black hole ‘scrambles’ the information with the rest of what’s already inside, and spits it out in record time — no system in Nature can do it faster! The phenomenon of chaos is an important component of the scrambling process: the ‘butterfly effect’ seems to be the underlying mechanism by which information gets scrambled by the black hole.

A black hole can be mathematically described as a bunch of particles that interact very strongly among themselves. In this paper the authors started with such a system, and then tuned the interactions to the opposite limit — in which they are very weak and the dynamics is classical. They studied how this weakly-coupled system scrambles information by studying its chaotic behavior. And they  found that the scrambling of information still happens very quickly (in a certain technical sense), even though the weakly-coupled system is far from the black hole regime. Their finding confirms a previous conjecture.

Chaotic behavior in weakly-coupled systems is a rich subject about which much is known. For example, the rate at which entropy is produced in weakly-coupled systems is an interesting observable that is known to be related (in a precise technical sense) to chaos. In our work we pointed out a set of such chaotic observables, and raised the question of how they are manifested in black holes. This is an open question which the authors plan to return to in the future.