The Fuzzball Fix for a Black Hole Paradox (2024)

In the late 18th century, the scientist John Michell pondered what would happen if a star were so massive, and its gravity so strong, that its escape velocity would be equivalent to the speed of light. He concluded that any emitted light would be redirected inward, rendering the star invisible. He called these hypothetical objects dark stars.

Michell’s 1784 treatise languished in quiet obscurity until it resurfaced in the 1970s. By then, theoretical physicists were well acquainted with black holes—the dark star idea translated into Albert Einstein’s theory of gravity. Black holes have a boundary called an event horizon that represents the point of no return, as well as a singularity, a point of infinite density within.

Yet Einstein’s description of the world is inconsistent with quantum mechanics, driving physicists to seek a complete theory of quantum gravity to reconcile the two. String theory is a leading contender, presenting yet another potential picture: Black holes may be reimagined as “fuzzballs,” with no singularity and no event horizon. Rather, the entire region within what was envisioned as the event horizon is a tangled ball of strings—those fundamental units of energy that string theory says vibrate in various complicated ways to give rise to space-time and all the forces and particles therein. Instead of an event horizon, a fuzzball has a “fuzzy” surface, more akin to that of a star or a planet.

Samir Mathur, a string theorist at Ohio State University, believes fuzzballs are the true quantum description of a black hole and has become a vocal champion of his own self-described “fuzzball conjecture” expanding on the concept. His version of fuzzballs provides potential mechanisms to resolve the knotty problem of reconciling the classical and quantum descriptions of a black hole—and, ultimately, the rest of our universe. But to make it work, physicists will have to abandon long-held notions of singularities and event horizons, a sacrifice many are unwilling to make.

Missing Entropy

Mathur’s work grew out of attempts to calculate the quantum properties of a black hole, as well as an ongoing struggle to resolve a paradox about what happens to information that falls into one. Both issues arise from Stephen Hawking’s insistence in the 1970s that black holes are not truly black. Due to quirks of quantum mechanics, they radiate a small amount of heat—called “Hawking radiation”—and thus have a temperature. If black holes have temperature, they must have entropy, often described as a measure of how much disorder is present in a given system. Every physical object has entropy, and entropy must always increase, per the second law of thermodynamics. Yet the smooth, featureless picture of a black hole described by general relativity doesn’t account for its entropy, which is a key feature of its quantum mechanical description.

An object’s entropy is described by microstates: the number of ways atoms can be rearranged to achieve the same macroscale object. A scrambled egg has more entropy than an unbroken egg because the scrambled egg’s atoms can be moved around in a seemingly infinite number of ways. By contrast, the distinct yolk and white in an unbroken egg limits the possibilities for atomic-level rearrangement.

Black holes are not exempted from the laws of thermodynamics. “Entropy comes from counting the [possible] states of atoms,” explained Joseph Polchinski, a physicist at the University of California, Santa Barbara. “So black holes should have some kind of atomic structure with countable states.” The problem is that any one black hole has far more possible states than thousands of scrambled eggs. The calculation required to measure entropy on that scale is truly daunting. It is possible to infer the number of states, however, using a formula devised by Jacob Bekenstein in 1972 that showed the entropy of a black hole to be proportional to the size of the event horizon around it.