Paper of the day: "Damn it! Why wasn't me to write this??"

One of my favorite songwriters, now retired Francesco Guccini, wasn't used to sing pieces written by other authors. One of the rare occasions in which he decided to do so is this one:

where he sings Roberto Vecchioni's "Luci a San Siro". Guccini's incipit starts by saying some like 

"The song I am going to sing is titled: - Damn it! Why wasn't me to write this song? 

... Well, the paper I am going to review today is titled"

"Damn it! Why wasn't me to write this paper?"

The paper I am referring to appeared some days ago on the arXiv,

it is written by Carlos Herdeiro and Eugen Radu from the University of Aveiro. I have to admit it, this paper is just beautiful. Seriously. Not only the result circumvents one of the classical theorems of General Relativity [the black hole no-hair theorem, see below] but, in doing so, it also connects elegantly two solutions which were previously thought to be very different. As if that was not enough, it is beautifully written in such a way that the overall feeling is the one that only great papers can give -- a feeling that only scientists have the privilege to appreciate [and possibly artists can do so too, while watching/listening to//performing other colleagues' pieces of arts as in the video above]. 

And, believe me, I write this with some note of jealousy, because the subject touches many topics I worked on in the last years. Only after having read the paper [sic], the result have appeared so clear that it now seems impossible they were missed until now. I guess this is common to remarkable papers. Anyway, this explains the title of this post, I guess.

Now, back to the paper. The main result is probably that John Archibald Wheeler (the father of the word "black hole") was wrong when he pronounced his famous sentence "Black holes have no hair". We have briefly explained what this is about in this post. In few words, up until now people thought that black holes in Einstein's theory were only described by 3 quantities: mass, spin and electric charge. This would apply to all black holes in the Universe (more precisely, to those in a stationary configuration), no matter how big they are and how they have been formed. 

In the last forty years people like Stephen Hawking, Jacob Bekenstein, Wheeler himself and many others tried to add "charges" (or some "quantum number") to black holes, for example putting some new field close to the event horizon and trying to "dress" the black hole. The Standard Model of particle physics (and its extensions) is not short of fields: fermions (like electrons and neutrinos), scalars (like the Higgs bosons), massive bosons (like the W and Z particles) were all used to try to create new black holes, perhaps more complicated than the simple ones predicted by Einstein's theory. The result of this tour-de-force was that the black hole "eats" the field very fast, deforms a little bit, but quickly returns in its original state after emitting some gravitational wave (exactly, something like those observed by BICEP2 some days ago). After many attempts, people were so sure that black holes cannot grow "hair" that Wheeler's no-hair conjecture is sometimes elevated to the status of a "theorem".

However, theorems can (and in fact often are) evaded by relaxing some of their assumptions in a smart way. In the case of this paper, the authors noted that the no-hair theorem requires not only the black hole to be stationary, but it requires matter around it (the new "hair") to be stationary as well. By relaxing this assumption, the authors shows that stationary black holes can co-exist with oscillating fields sourced by some charge at the event horizon.

There is an extra ingredient for this "hairy black hole recipe". The black hole has to be spinning. This is requested because the centrifugal force associated to the rotation can balance gravity and sustain the extra field, which would otherwise be eaten by the event horizon in the static (non-rotating) case.

So far so go, but there's even more. Finding these solutions requires to solve Einstein's equations (which are notoriously very complicate) on a computer. This requires a lot of assumptions and a lot of work: it is not an exercise that everyone would undertake without a strong motivation. So, how did the authors guessed that the hypothesis they used were just the right one? They didn't, of course, and this brings me back to the hint that everybody could have seen and that it is so clear only after this work.

The authors used a massive scalar field. Since the 70s, it is known that such field triggers an instability of spinning black holes. Basically, this instability implies the existence of a critical value of the spin of the black hole, above which the object becomes unstable. The word "critical" is crucial here. It means that if the spin is tuned precisely to the critical value, the black hole is on the verge to become unstable. These critical points are often associated to phase transitions, like in phase diagrams:

From Wikipedia: the vapor–liquid critical point in a pressure–temperature phase diagram is at the high-temperature extreme of the liquid–gas phase boundary. The dotted green line shows the anomalous behavior of water.

In other words, at critical points multiple solutions can "co-exist". In our case one solution is the standard Kerr black hole of General Relativity, whereas the other is supposedly a new solution that nobody discovered before. This intuition turned out to be correct and it has allowed the authors to construct their new solution.

An there is even more! These new black holes have an extra "scalar charge" that makes them violate the uniqueness theorem (that is, there can exist two black holes with same mass and spin, but that differ from each other because they have different scalar charges). The new solution can be interpreted as a black hole immersed in an oscillating scalar field. This oscillating field (without the black hole) was also known since the 60s and it is called "boson star". The results of this paper show that spinning boson stars and Kerr black holes are like the two extrema of a continuous family of solutions, which is precisely interpolated by the hairy black holes found in this paper.

Boson stars and black holes have been studied for decades now, and yet nobody found this elegant connection before. It's like if these boson stars and the Kerr black holes were cousins, but nobody realized that before, because the genealogical connection was missing. These new solutions are the missing link.

There is something much more profound here, that is true in all areas of physics (and mathematics). This result shows how deep a theorem (and violation therein) can be in physics: by finding a smart way to evade it, new paths magically open, spectacular connections just pop up and the outcome will surely have implications that the community is called to understand.

Congratulations go to the authors!