We knew black holes have a temperature. It turns out they have a pressure too

In classical general relativity, black holes are relatively simple objects. They can only be described by three properties: mass, charge and rotation. But we know that general relativity is an incomplete theory. Quantum mechanics is most evident in the behavior of tiny objects, but it also plays a role in large objects such as black holes. To describe black holes at the quantum level, we need a theory of quantum gravity. We don’t have a complete theory yet, but what we do know so far is that quantum mechanics makes black holes more complex and gives them properties like temperature and maybe even pressure.

Temperature is perhaps the best-known quantum property of a black hole. Because of the uncertainty of quantum particles, energy cannot be fully bound to the event horizon of a black hole. Sometimes energy can escape its gravitational prison through a process known as Hawking radiation. The amount of energy escaping is tiny, but it means that black holes have a (very cold) temperature. And that means that black holes can be described using the laws of thermodynamics. For regular matter, thermodynamics describes not only the temperature of an object, but also properties such as pressure. This is where this new study comes in.

The team studied a thermodynamic property known as entropy. Entropy is a subtle concept that is often described as a measure of a system’s disorder or the amount of information needed to describe a system. It refers to the temperature of an object through the second law of thermodynamics. With black holes, entropy refers to the surface of an event horizon. Physicists study the entropy of black holes because it could help us answer fundamental questions about quantum gravity, such as whether a black hole can destroy information.

So the team applied entropy equations to a simple black hole to find out what happens when you extend Einstein’s equations to quantum theory, which is a common trick known as the semi-classical approach. As they did this, they kept getting weird extra expressions in their equations that they weren’t expecting. These terms didn’t make sense until the team looked at them under pressure. It turned out that the additional terms act like pressure on a black hole, just as gas atoms create pressure in a container. In other words, if you apply quantum theory to a black hole, you will get both temperature and pressure.

As with the Hawking temperature, this quantum pressure is extremely small for a black hole. It is far too small to affect the types of black holes we see in the universe. But the fact that it exists could have real ramifications for the most extreme regions of the cosmos, like the Big Bang. This particular model is too simple to apply to real systems, but it’s an interesting clue to a more complete theory of quantum gravity.

Reference: Xavier Calmet, et al. “Quantum gravitational corrections to the entropy of a Schwarzschild black hole.” Physical verification D 104.6 (2021): 066012.