In the Area Again

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Hawking radiation has never been proved, but it’s generally thought to be real. Essentially, the argument is that when you combine black hole event horizons with quantum fuzziness, thermal energy can escape a black hole. We don’t have a fully quantum theory of gravity, but we do have several semi-classical models that support the existence of Hawking radiation. And if Hawking radiation is true, then the interaction of black holes is governed by the laws of thermodynamics.

The argument is pretty simple. If black holes quantum radiate, then they emit heat energy and have a thermal temperature. So the laws of thermodynamics apply to black holes just as they do to a really hot cup of tea. This idea is incredibly powerful because it means the complex interactions of merging black holes can be described as black hole thermodynamics.

In simple terms, there are four basic laws of thermodynamics:

Zeroth: If objects A-C and B-C are in thermal equilibrium, then so is A-B.

First: Energy is conserved, so thermal energy lost by an object is gained by others.

Second: Heat energy naturally flows from hotter objects to colder objects, not the other way around. This is often stated as “the entropy of a system can never decrease.”

Third: You can never cool an object to absolute zero.

For black holes, these laws become:

Zeroth: A non-rotating black hole has uniform gravity at its event horizon.

First: The temperature—and therefore entropy—of a black hole is determined by the surface area of its event horizon.

Second: Since entropy can never decrease, the surface area of a merged black hole must be no less than the surface area of the two original black holes.

Third: You can’t remove the event horizon of a black hole by spinning it up or giving it an electric charge.

Tang, et al

The second law is also known as the Area Theorem for black holes, and in many ways it’s the most powerful. Black holes can emit several stars’ worth of gravitational wave energy when they merge. It’s the reason we can detect them. But the Area Theorem says there is a hard limit to the amount of gravitational energy mergers can produce. The final black hole must have at least the same surface area as the originals. And since the surface area of a black hole’s event horizon depends upon its mass, that means the mass of a merger is likewise constrained.

The good news is that the Area Theorem is something we can test by looking at black hole mergers. Back in 2021, a study of the black hole merger GW150914 supported the Area Theorem with a 97% confidence level.¹ Now a new study of the merger GW230814 confirms the theorem to a 99.5% confidence level.² Both of these results are less than the usual 5σ level used for scientific certainty, which would be a 99.99994% certainty, but the results are still quite strong.

Black hole thermodynamics seems to be true, which is an astonishing idea when you think about it. It means when you have a hot cuppa on a cold morning, the same physics that warms your hands steers the dynamics of black hole event horizons.