Image: Black hole, Credit: Canva

Black holes have no hairs, literally!

GABRIELE FALCINELLI
Sept. 7, 2021

When you talk about science there are some discoveries made quickly and others made gradually, as a result of the work of many scientists over long years invested in research. This of the lack of hairs on black holes is of the second type; today, in this article I will explain what this ambiguous phrase means and you will uncover much interesting stuff about black holes, so make yourself comfortable and take about ten minutes to read this.

The first pointers that 'black holes have no hairs' came up in 1964 thanks to Vitaly L. Ginzburg, who in previous years had worked in the URSS for the construction of the hydrogen bomb, inventing the LiD (deuterated of lithium).

He examined a sequence of magnetized static stars (stars with a magnetic field & without any rotational speed) increasingly compact, until he observed that when the circumference of the star reached its critical value and transforms itself into a black hole, the lines of the magnetic field were sucked inside its event horizon, leaving the blackhole completely devoid of any magnetic field. This, therefore, suggested an intriguing possibility: black holes originated from magnetized stars may not have any magnetic field.

Meanwhile, moving a few kilometers away from Ginzburg’s laboratory, we find in Moscow the team of Yakov Zel’dovich, headed by Igor Novikov and Andrei Doroshkevich. Making a short recall we should say that this group of highly qualified scientists had succeeded in planning and constructing, during the period of the Second World War, the first hydrogen bomb ever built. Now, when the war ended, despite Russia remained a fairly rigid and detached country from the West, numerous modern challenges have been accepted regarding the wider fields, especially in the astrophysical, physical and mathematical ones.

So our soviet team asked itself a question: "Since the implosion of a round star produces a round black hole, then will a deformed star produce a deformed black hole?". To give an extreme example: "Will the implosion of a cubic star generate a cubic black hole?”.

Then the calculations began, but these are expected to be extremely complex in the case of a square or a particularly deformed and, even more, rotating star, so Zel'dovich's team considered a simplified case of a non-rotating hemispherical star with a small mountain on the surface. Moreover, instead of simulating the entire dynamic implosion of the star, they examined a sequence of static stars (without any rotation) more and more compact, further reducing the complexity of the calculations and finally obtaining an answer: when a static star, with a little mountain is small enough to form a black hole, the event horizon of the hole must be perfectly spherical without any protrusion. It has been attempted to give an answer also in relation to the square star, but there were no mathematical proves. Anyway, if a cubic star, imploding, gives rise to a spherical black hole, then there won’t be a way, observing a generic black hole, to understand the shape of its original star before its collapse.

Slowly but steadily the studies began leading to results, but there was still a lot to process before actually understanding if black holes were always spherical or not. Afterward, a few years later from the beginning of this study, the American physicist John Wheeler, with his originality and imagination gave a name to this whole unit, and, based on the discoveries that had already been made he coined the following expression: "Black holes have no hairs". I hope you won’t stop reading here, but that you’ll continue until you get the true, sure, and proved the answer to this statement.

For the record, in 1965 the first edition (in Russian language) of the hairless black hole conjecture was published by Zel’dovich’s team, showing the analysis carried out strictly. The first part of the work, written by Doroshkevich and Novikov, was the mathematical demonstration that, when a static star with a small mountain becomes more and more compact, there were only two possible results: either the star created a perfectly spherical black hole around itself, or the mountain would have produced an enormous curvature of the spacetime fabric, making the result of the implosion unknown.

The potency of controversial research is huge: it attracts scientists as light does with moths; that’s what happened with the evidence of the lack of hairs on black holes are given by Zel’dovich’s team.

The first scientist coming to apply in these studies was Werner Israel, born in Berlin and grown in South Africa, after becoming an expert in the Relativity field. After many efforts he not only analyzed small mountains, as the Soviets did but also mountains of every shape and form, making his calculations perfectly work for every type of implosion, as well for a cubic star.

Undoubtedly his research was more complete than the one published in 1965 by Doroshkevich and Novikov, providing a very similar response, but a more purposeful one: a highly not spherical implosion provides only two possible results: a black hole is either not formed or a perfect spherical one is born. However, it needs to be addressed that this conclusion was only effective if the body that was imploding didn’t have any electric charge or any rotational speed.

Israel presented his examinations, for the first time on the 8th February 1967, during a conference at the King's College in London. Here from an ex-student of J. Wheeler, a question arose: “What happens if the star rotates and it has an electric charge?”

From the impression to obtain the answer by now, you fell back down again in doubt. And now? Let’s try to go after what we’ve already spoken about: until now we surely know that a non-rotational black hole, with an electric charge, is still spherical, albeit its original star was so deformed to be a cube. But how can a black hole get the gravitational influence of any contingent mountains off? Using other words, what is causing the black hole to be spherical?

Well, the response to these questions was published on the 27th of August 1970 by Jack Smith: a smooth reporter of the “Los Angeles Times”, after his field trip at the Caltech. As a matter of fact, this research had started to be a pretty coveted one in the scientific community, so after Novikov and Israel, Richard Price, from Brooklyn arrived. Subsequently, he stated his theorem about the reason why black holes haven’t any protrusion on the event horizon’s surface: “What can be radiate must be radiate”.

Let’s dive into it explaining what does it mean: considering a generic star with a small mountain on its surface, Price has demonstrated that, when the star implodes restricting its circumference, the mountain gets expanded producing a bigger deformation of the spacetime fabric. After the star reached its critical circumference becoming a black hole, the mountain starts shrinking until it disappears forever in the form of gravitational waves.

To make this clear I want to make a fitting example: imagine putting your finger on a guitar’s string pulling it; obviously after have removed your finger the string will start swinging and vibrating, emitting sound waves as the mountain does with the black hole. However, it’s important to consider these questions: “If everything that can be radiate must be radiate, what will remain? What cannot be radiate?”.

As all the physicists know, in physics, there are specific laws called “of conservation” for which some quantities, that can never oscillate or vibrate in a radiative way, do exist. Those are the mass (which thanks to the equation E=mc2 is interchangeable with energy), the angular momentum (which corresponds to the rotational speed), and the electric charge (which determines the orientation of the electric field). So, finally, Price’s theorem ensures the conversion of any black hole’s protrusion into gravitational waves every time!

Now we know how a generic black hole transforms the imperfections of its main star into gathers of the space-time curvature, nevertheless, Price’s analysis was limited only to stars which were imploding with a very slow rotational speed and almost perfectly spherical: it was just the explanation of protrusion’s future conditions.

The ultimate prove of the lack of hairs on black holes was finally provided by Brandon Carter, Stephen Hawking and Werner Israel. So, after more than 15 years, the studies which are today the evidence of the: “No hair-theorem” has been ended, describing also the process on high rotational-speed stars.

Also if a black hole is deformed thanks to its high rotational speed (the only thing which can give a deformation to the event horizon), the black hole will always maintain the same star’s mass, momentum and charge thanks to them it’s possible to describe the state of a generic black hole and its properties. On the other hand, it has been noticed that the electric charge does not produce any property’s mutation, so it simply not even considered.

Conclusion

In conclusion, black holes are pretty simple cosmic bodies depicted by clear mathematical laws although the interest related to their singularity gives them such a mysterious entity, that  many scientists think they’re hiding the secret of the marriage between General Relativity and Quantum Mechanics, and so the bond of “the extremely big and the extremely small”…but who will find the answer?? As we’ve seen in this article, everything begins with a simple question, but then it’s your turn to give it an answer!