# Black holes have to be renamed

## "Soft Hair" on Black Holes: Stephen Hawking's Last Big Idea

Stephen Hawking has studied black holes all his life and made groundbreaking theoretical discoveries, such as radiation that is named after him. His last big hit, "soft hair" on black holes, resulted in a remarkable competition of ideas between Cambridge University, Harvard University, Université libre de Bruxelles and my research group at TU Wien.

### Hairy properties

Physicists can be very creative in naming complex issues. A master of naming was John Wheeler, who coined the term "black hole" as well as the slogan "black holes have no hair". To understand "soft hair", let's start with Wheeler's slogan - what does "hair" mean in this context?

Every sufficiently large object - for example bacteria, people or suns - has a wealth of properties that characterize it. "Hair" is a metaphor for all these properties, as it takes a lot of information to describe hair: length, color, hair thickness, etc. - and that for each individual hair. Black holes are an exception. Like elementary particles, they are fully characterized by just three numbers: their mass, their angular momentum and their charge. This fact is expressed through Wheeler's slogan.

**Hawking's discovery**

Now one could shrug one's shoulder and reply: "Okay, black holes are as simple as elementary particles despite their size - why does theoretical physics make such a drama out of them and introduce hairy metaphors?" Quantum mechanics provides the answer.

In 1972 Jacob Bekenstein made the suggestion, absurd at the time, that black holes have gigantic entropy. Entropy is information, i.e. bits and bytes in computer science slang. If you ask what the most efficient computer you can ever build (an object with the highest possible information density), Bekenstein's answer is: a black hole. The problem with Bekenstein's thesis was that every object with entropy and mass must also have a temperature, and everything that has temperature radiates - but it was known that nothing can escape from a black hole.

This is where Hawking came in. His greatest discovery in 1974/75 overturned the last conclusion. Using quantum field theoretical calculations in the background of a black hole, he determined that something can escape from a black hole if you allow quantum fluctuations - and you don't really have a choice here, because our universe is quantum mechanical. Hawking's calculations show that black holes actually have a temperature - the Hawking balance temperature - that they have gigantic entropy - the Bekenstein-Hawking entropy - and that they emit Hawking radiation.

**Large information store**

So we are in the remarkable situation that black holes without quantum mechanics are the simplest objects in the universe, since they have no "hairs", but with quantum mechanics they are the most complicated objects that can exist in the universe - there are, with the same size, nothing that can have more entropy than a black hole.

Hawking's calculation was the beginning of a technical and conceptual tour de force - from the information paradox to the holographic principle to "soft hair" - which is still ongoing today. Unsolved puzzles of quantum gravity - the "Holy Grail" of theoretical physics - mostly relate to black holes, raising the question of why black holes can store so much information and how exactly they do it.

**Soft hair**

Stephen Hawking's last big idea - in collaboration with Malcolm Perry and Andrew Strominger - sheds new light on these questions. "Soft hair" is a synonym for distinguishable structure without energy. Usually every form of structure has at least a little bit of energy (every bit you want to store somewhere needs a minimum amount of energy, no matter how you store it), but the new concept of "soft hair" allows structure without changing the energy . Hawking, Perry, and Strominger claim that even without considering quantum mechanics, black holes can have hair as long as they are soft.

Is that correct? And, if so, what exactly does soft hair look like and does it help us understand the entropy of black holes? I answer these questions in detail from a personal point of view in the style of a diary.

**Black flowers**

Here is a short summary: For black holes in only two spatial dimensions, we were able to show in 2016 that soft hair actually exists. If you think of a black hole as a circle, then soft hair is a periodic deformation of this circle - my Chilean co-workers like to refer to this object as a "black flower".

We were able to show that each of these black flowers has the same energy as the corresponding black hole - that is, the "petals" are "soft" in the sense of Hawking, Perry and Strominger, as long as the average radius of the black flower is not changed. So it is true that black holes can have soft hair - they then turn into black flowers, indistinguishable from black holes to distant observers.

In 2017, together with Iranian employees, we succeeded in counting all black flowers that look like a black hole with a certain mass and angular momentum to distant observers. Using assumptions that are reminiscent of Bohr's quantization rules, we were able to reduce the problem of the entropy of black holes to a combinatorial problem that was solved exactly 100 years ago by the mathematicians Godfrey Hardy and Srinivasa Ramanujan. Counting these black flowers using the Hardy-Ramanujan formula gave exactly the Bekenstein-Hawking entropy formula.

Hawking's last big hit works at least for simple black holes - whether this also applies to black holes of astrophysical interest is the subject of current research. (Daniel Grumiller, November 7, 2018)

**Daniel Grumiller **is Professor of Theoretical Physics at the TU Wien, where he has headed the "Black Holes" research group since 2009. He was elected a member of the Young Academy of the Austrian Academy of Sciences in 2013 and was a member of the board of directors from 2014 to 2016.

**link**

- Young Academy of the OeAW (constituted in 2008 as a Young Curia as part of the modernization of the OeAW, renamed to Junge Akademie / Young Academy in 2016); Video; Brochure; Twitter: @ya_oeaw

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