According to general relativity, the inward gravitational collapse never stops. Even though, from the outside, the black hole appears to stay a constant size, expanding slightly only when new things fall into it, its interior volume grows bigger and bigger all the time as space stretches toward the center point. For a simplified picture of this eternal growth, imagine a black hole as a funnel extending downward from a two-dimensional sheet representing the fabric of space-time. The funnel gets deeper and deeper, so that infalling things never quite reach the mysterious singularity at the bottom. In reality, a black hole is a funnel that stretches inward from all three spatial directions. A spherical boundary surrounds it called the “event horizon,” marking the point of no return.
Since at least the 1970s, physicists have recognized that black holes must really be quantum systems of some kind—just like everything else in the universe. What Einstein’s theory describes as warped space-time in the interior is presumably really a collective state of vast numbers of gravity particles called “gravitons,” described by the true quantum theory of gravity. In that case, all the known properties of a black hole should trace to properties of this quantum system.
Indeed, in 1972, the Israeli physicist Jacob Bekenstein figured out that the area of the spherical event horizon of a black hole corresponds to its “entropy.” This is the number of different possible microscopic arrangements of all the particles inside the black hole, or, as modern theorists would describe it, the black hole’s storage capacity for information.
Bekenstein’s insight led Stephen Hawking to realize two years later that black holes have temperatures, and that they, therefore, radiate heat. This radiation causes black holes to slowly evaporate away, giving rise to the much-discussed “black hole information paradox,” which asks what happens to information that falls into black holes. Quantum mechanics says the universe preserves all information about the past. But how does information about infalling stuff, which seems to slide forever toward the central singularity, also evaporate out?
Read: Seeing a black hole through Stephen Hawking’s eyes
The relationship between a black hole’s surface area and its information content has kept quantum-gravity researchers busy for decades. But one might also ask: What does the growing volume of its interior correspond to, in quantum terms? “For whatever reason, nobody, including myself for a number of years, really thought very much about what that means,” said Susskind. “What is the thing which is growing? That should have been one of the leading puzzles of black-hole physics.”
In recent years, with the rise of quantum computing, physicists have been gaining new insights about physical systems such as black holes by studying their information-processing abilities—as if they were quantum computers. This angle led Susskind and his collaborators to identify a candidate for the evolving quantum property of black holes that underlies their growing volume. What’s changing, the theorists say, is the “complexity” of the black hole—roughly a measure of the number of computations that would be needed to recover the black hole’s initial quantum state, at the moment it formed. After its formation, as particles inside the black hole interact with one another, the information about their initial state becomes ever more scrambled. Consequently, their complexity continuously grows.