Black holes: Hawking confirmed

This post is about the recently reported experimental confirmation of a theoretical prediction of Stephen Hawking about black holes. First a bit about the theorem, and then the experiment:

1. Hawking's area law: A black hole is a region in space where matter has been compressed to such a small volume that nothing, not even light, can escape its gravitational pull.

   
   

   Black holes are interesting since the effects of gravity - which are typically weak elsewhere in the universe - are extreme in their case. Therefore, their study can tell us about the nature of the gravity (and possibly its relation to quantum mechanics), the dynamics of galaxies, the character of spacetime, etc, etc.

   
   

   A black hole is not a point-like object; it has a boundary at a nonzero radius. If anything approaches closer than this boundary, it cannot escape the black hole. This boundary is called the event horizon of the black hole. We can think of the event horizon as a sphere surrounding the black hole, out at some radius.

   
   

   Now, the second law of thermodynamics says that disorder (more technically entropy) cannot decrease in the universe. But we could throw a disordered system (like my clothes closet) into a black hole and then the total entropy of the universe would decrease. This would violate the second law of thermodynamics.

   
   

   The second law could be saved, realized Jacob Bekenstein, if the black hole carried its own entropy and it registered an increase larger than the entropy of the object being thrown into it. This would result in a net increase of the entropy of the universe and thus save the second law. Now Bekenstein knew of Stephen Hawking's theorem, derived from classical general relativity in 1971, that the surface area of a black hole event horizon never decreases. He put two and two together in 1972 and argued that a black hole's entropy should be proportional to the surface area of its event horizon.

   
   

   Hawking himself opposed Bekenstein's idea initially. He argued that black holes cannot have entropy as they do not have temperature and do not emit radiation. But he realized that this was only true if he took the laws of classical physics into account. When he included quantum mechanics in his calculation, he found that black holes indeed have temperature, emit (Hawking) radiation and possess entropy. The formula for the temperature of a black hole is now engraved on Hawing's gravestone at Westminster Abbey.

   
   

   A simple demonstration of Hawking's area law: throw a black hole into another black hole. The result? A third black hole, of course. The area law says that the event horizon area of the resulting black hole is larger than the sum of the areas of the two original black holes. And this is exactly what the experiment observed.

2. The experiment at LIGO: As its name says, the Light Interferometer Gravitational Wave Observatory can detect gravitational waves (the work I am referring to is a collaboration with VIRGO and KAGRA). Interestingly, the collision - coalescence - of two black holes releases gravitational waves as a way of shedding energy and angular momentum.

   
   

   The pre- and post-merger gravitational wave signals - which contain information about the frequencies and damping rates of the black hole oscillation modes - can be used to infer the mass and spin of each black hole. And mass and spin are the only two parameters we need to know to characterize these black holes - in this sense black holes are astonishingly simple objects. In fact, Equation 1 in the LIGO paper quotes the beautifully compact formula for the event horizon area in terms of the black hole mass and spin. Plugging their data into this formula, the experimentalists confirmed Hawking's area theorem.

   
   

   Afterword

   
   

   As you may expect, Hawking radiation causes a black hole to radiate - shrink its event horizon area - and eventually evaporate into nothing. So Hawking's area theorem should perhaps be stated in a more refined manner: any process that increases the mass of a black hole cannot decrease its entropy and hence its event horizon area. For more nuances, read the paper.