###### Blog

# In the Area

5 July 2021

On its own, a black hole is remarkably easy to describe. The only observable properties a black hole has are its mass, its electric charge (usually zero), and its rotation, or spin. It doesn’t matter how a black hole forms. In the end, all black holes have the same general structure. Which is odd when you think about it. Throw enough iron and rock together and you get a planet. Throw together hydrogen and helium, and you can make a star. But you could throw together grass cuttings, bubble gum, and old *Harry Potter* books, and you would get the same kind of black hole that you’d get if you just used pure hydrogen.

This strange behavior of black holes is known as the no hair theorem, and it relates to what’s known as the information paradox. In short, since everything in the universe can be described by a certain amount of information, and objects can’t just disappear, the total amount of information in the universe should be constant. But if you toss a chair into a black hole, it just adds to the black hole’s mass and spin. All the information about the color of the chair, whether it’s made of wood or steel, and whether it’s tall or short is lost. So where did that information go?

One solution to this information paradox could be possible thanks to Stephen Hawking. Back in 1974, he demonstrated that the event horizon of a black hole might not be absolute. Because of quantum indeterminacy, black holes should emit a tiny amount of light now known as Hawking radiation. Hawking radiation has never been observed, but if it exists the information lost when objects enter a black hole might be carried out of the black hole via this light. Thus the information isn’t truly lost.

If Hawking radiation is real, that also means that black holes follow the laws of thermodynamics. It’s an idea first proposed by Jacob Bekenstein. If black holes emit light, then they have to have a thermal temperature. Starting from Bekenstein’s idea, several physicists have shown that there is a set of laws for black holes known as black hole thermodynamics.

Since you’re reading this article, you’re probably familiar with the second law of thermodynamics, which states that the entropy of any system must increase. This is the reason that a cup of hot coffee cools down over time, slightly heating the room until the coffee and the room are all the same temperature. You never see a cold cup of coffee spontaneously heat up while slightly cooling the room. Another way to state the second law is that heat flows from a hot object to surrounding cooler objects.

For black holes, the second law of thermodynamics applies to the area of a black hole’s event horizon. The Hawking temperature of a black hole is related to this area. The larger the black hole, the lower its Hawking temperature. So the second law of black hole thermodynamics says that for any black hole merger the entropy must increase. That means the surface area of the resulting black hole must be greater than the surface areas of the two original black holes combined. This is known as *Hawking’s Area Theorem*.

Of course, all of this is a bunch of mathematical theory. It’s what we expect given our understanding of physics, but proving it is a different matter. Now a study in *Physical Review Letters* has given us evidence that it’s true.^{1} The team looked at the very first observation of two merging black holes. The event is now known as GW150914 and was a merger of a 29 solar-mass black hole with a 36 solar-mass one. Using a new analysis method on the gravitational waves they produced, the team was able to calculate the event horizon surface areas for the original black holes. When they compared them to the surface area of the final 62 solar-mass black hole, they found the total area increased.

The results have a confidence level of 97%, which is good but not strong enough to be considered clinching proof. But this method can be applied to other black hole mergers, and it is the first real evidence that black hole thermodynamics is more than just a theory.

Isi, Maximiliano, et al. “Testing the black-hole area law with GW150914.”

*Physical Review Letters*127.1 (2021): 011103. ↩︎