One of Stephen Hawking’s most famous theories has been confirmed to be correct, thanks to space-time ripples caused by the merger of the two distant black holes.
The black hole area theorem, which Hawking derived from Einstein’s theory of general relativity in 1971, states that the surface area of a black hole cannot decrease over time.
This rule is of importance to physicists because it appears to set time to run in a certain direction: the second law of thermodynamics, which states that the entropy, or disorder, of a closed system, must always rise. Because the entropy of a black hole is proportional to its surface area, both must always increase.
The researchers’ confirmation of the area law, according to the new study, appears to suggest that the properties of black holes are crucial hints to the hidden laws that control the universe. Surprisingly, the area law appears to contradict another of the famous physicist’s proven theorems: that black holes should evaporate over incredibly long time scales, suggesting that determining the source of the conflict between the two theories might reveal new physics.
“A black hole’s surface area can’t be decreased, which is like the second law of thermodynamics. It also has a conservation of mass, as you can’t reduce its mass, so that’s analogous to the conservation of energy,” lead author Maximiliano Isi, an astrophysicist at the Massachusetts Institute of Technology, told. “Initially people were like ‘Wow, that’s a cool parallel,’ but we soon realized that this was fundamental. Black holes have an entropy, and it’s proportional to their area. It’s not just a funny coincidence, it’s a deep fact about the world that they reveal.”
The event horizon limits the surface area of a black hole; beyond this point, nothing, not even light, can escape its strong gravitational pull. According to Hawking’s interpretation of general relativity, as a black hole’s surface area increases with its mass, and because no object thrown inside can exit, its surface area cannot decrease.
However, because the surface area of a black hole reduces as it spins, researchers questioned if it would be feasible to throw an object inside hard enough to cause the black hole to spin enough to diminish its area.
“You will make it spin more, but not enough to counterbalance the mass you’ve just added,” Isi said. “Whatever you do, the mass and the spin will make it so that you end up with a bigger area.”
To put this idea to the test, the researchers examined gravitational waves, or ripples in the fabric of space-time generated 1.3 billion years ago by two massive black holes spiralling toward each other at high speeds.
The Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO), a laser beam divided into two 2,485-mile-long (4-kilometer) pathways capable of detecting the slightest distortions in space-time by how they affect its path length, discovered the first waves in 2015.
The researchers determined the mass and spin of both the two original black holes and the new combined one by dividing the signal into two parts — before and after the black holes merged. These figures enabled them to compute the surface area of each black hole before to and after the collision.
“As they spin around each other faster and faster, the gravitational waves increase in amplitude more and more until they eventually plunge into each other — making this big burst of waves,” Isi said. “What you’re left with is a new black hole that’s in this excited state, which you can then study by analyzing how it’s vibrating. It’s like if you ping a bell, the specific pitches and durations it rings with will tell you the structure of that bell, and also what it’s made out of.”
The newly formed black hole has a greater surface area than the first two combined, proving Hawking’s area rule with higher than 95% certainty. According to the researchers, these findings are mostly consistent with their predictions. The theory of general relativity, from which the area law was developed, does an excellent job of characterizing black holes and other large-scale objects.
The real mystery however, begins when we try to integrate general relativity — the rules of big objects — with quantum mechanics — those of the very small. Strange events begin to occur, wreaking havoc on all of our hard and fast rules and entirely breaking the area law.
This is because, according to general relativity, black holes may shrink according to quantum mechanics. The famous British physicist behind the surface area rule also created the concept of Hawking radiation, which describes how a fog of particles is released at the edges of black holes due to strange quantum processes.
This phenomenon leads the black holes to shrink and, eventually, over a time period several times longer than the age of the universe, evaporate. This evaporation may occur over periods long enough to avoid violating area law in the short term, but that is little consolation to physicists.
“Statistically, over a long period of time, the law is violated,” Isi said. “It’s like boiling water, you’re getting steam evaporating from your pan, but if you only limit yourself to looking at the disappearing water inside of it, you might be tempted to say the entropy of the pan is decreasing. But if you take the steam into account too, your overall entropy has increased. It’s the same with black holes and Hawking radiation.”
After establishing the area rule for short to medium time frames, the researchers will evaluate data from more gravitational waves to get further insights into black holes.
“I’m obsessed with these objects because of how paradoxical they are. They’re extremely mysterious and confounding, yet at the same time we know them to be the simplest objects that exist,” Isi said. “This, as well as the fact that they’re where gravity meets quantum mechanics, makes them the perfect playgrounds for our understanding of what reality is.”