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and radiation, however messy and disordered, are crushed to infinitesimal size at a black hole’s center: a black hole is the ultimate in orderly trash compaction. True, no one knows exactly what happens during such powerful compression, because the extremes of curvature and density disrupt Einstein’s equations; but there just doesn’t seem to be any capacity for a black hole’s center to harbor disorder. And outside the center, a black hole is nothing but an empty region of spacetime extending to the boundary of no return—the event horizon—as in Figure 9.1. With no atoms or molecules wafting this way and that, and thus no constituents to rearrange, a black hole would seem to be entropy-free.

Figure 9.1 A black hole comprises a region of spacetime surrounded by a surface of no return, the event horizon.

In the 1970s, this view was reinforced by the so-called no hair theorems, which established mathematically that black holes, much like the bald performers of Blue Man Group, have a dearth of distinguishing characteristics. According to the theorems, any two black holes that have the same mass, charge, and angular momentum (rate of rotation) are identical. Lacking any other intrinsic traits—as the Blue Men lack bangs, mullets, or dreads—black holes seemed to lack the underlying differences that would harbor entropy.

By itself, this was a fairly convincing argument, but there was a yet more damning consideration that seemed to definitively undercut Bekenstein’s idea. According to basic thermodynamics, there’s a close association between entropy and temperature. Temperature is a measure of the average motion of an object’s constituents: hot objects have fast-moving constituents, cold objects have slow-moving constituents. Entropy is a measure of the possible rearrangements of these constituents that, from a macroscopic viewpoint, would go unnoticed. Both entropy and temperature thus depend on aggregate features of an object’s constituents; they go hand in hand. When worked out mathematically, it became clear that if Bekenstein was right and black holes carried entropy, they should also have a temperature.3 That idea set off alarm bells. Any object with a nonzero temperature radiates. Hot coal radiates visible light; we humans, typically, radiate in the infrared. If a black hole has a nonzero temperature, the very laws of thermodynamics that Bekenstein was seeking to preserve state that it too should radiate. But that conflicts blatantly with the established understanding that nothing can escape a black hole’s gravitational grip. Most everyone concluded that Bekenstein was wrong. Black holes do not have a temperature. Black holes do not harbor entropy. Black holes are entropy sinkholes. In their presence, the Second Law of Thermodynamics fails.

Despite the evidence mounting against him, Bekenstein had one tantalizing result on his side. In 1971, Stephen Hawking realized that black holes obey a curious law. If you have a collection of black holes with various masses and sizes, some engaged in stately orbital waltzes, others pulling in nearby matter and radiation, and still others crashing into each other, the total surface area of the black holes increases over time. By “surface area,” Hawking meant the area of each black hole’s event horizon. Now, there are many results in physics that ensure quantities don’t change over time (conservation of energy, conservation of charge, conservation of momentum, and so on), but there are very few that require quantities to increase. It was natural, then, to consider a possible relation between Hawking’s result and the Second Law. If we envision that, somehow, the surface area of a black hole is a measure of the entropy it contains, then the increase in total surface area could be read as an increase in total entropy.

It was an enticing analogy, but no one bought it. The similarity between Hawking’s area theorem and the Second Law was, in almost everyone’s view, nothing more than a coincidence. Until, that is, a few years later, when Hawking completed one of the most influential calculations