# What Are Some Advanced Black Hole Physics Topics?

*Leonard Kelley holds a bachelor's in physics with a minor in mathematics. He loves the academic world and strives to constantly explore it.*

## Cosmic Censorship Hypothesis

From 1965-1970, Roger Penrose and Stephen Hawking worked on this idea. It stemmed from their findings that a usual black hole would be a singularity of infinite density as well as infinite curvature. The hypothesis was brought into deal with the future of whatever falls into a black hole, besides spaghetitfication. You see, that singularity doesn’t follow physics as we know it and they break down once at the singularity. The event horizon around a black hole prevents us from seeing what happens to the black hole because we don’t have the light to know about the state of whatever fell in. Despite this, we would have a problem if someone crossed over the event horizon and saw what was happening. Some theories predicted that a naked singularity would be possible, which means a wormhole would be present that stops us form contacting the singularity. However, wormholes would be highly unstable, and so the weak cosmic censorship hypothesis was born in an attempt to show this was not possible (Hawking 88-9).

The strong cosmic censorship hypothesis, developed by Penrose in 1979, is a follow-up to this where we postulate that a singularity is always in the past or future but never in the present, so we cannot know anything about it presently past the Cauchy horizon, located beyond the event horizon. For years, scientists put their weight into this hypothesis because it allowed physics to work as we know it. If the singularity was beyond interfering with us then it would exist in its little pocket of space time. As it turns out, that Cauchy horizon doesn’t cut off the singularity as we had hoped, meaning that the strong hypothesis is false also. But not all is lost, for the smooth features of space time are not present here. This implies that the field equations can’t be used here and so we still have a disconnect between the singularity and us (Hawking 89, Hartnett “Mathematicians”).

## No-Hair Theorem

In 1967, Werner Israel did some work on non-rotating black holes. He knew none existed but like much of physics we start with simple models and build towards the reality. According to relativity, these black holes would be perfectly spherical and their size would only depend on their mass. But they could only arise from a perfectly spherical star, of which none exist. But Penrose and John Wheeler had a counter to this. As a star collapses, it emits gravity waves in a spherical nature as the collapse goes on. Once stationary, the singularity would be a perfect sphere no matter what shape the star was. The math supports this, but again we must point out this is just for non-rotational black holes (Hawking 91, Cooper-White).

Some work had been done on rotating ones in 1963 by Roy Kerr and a solution was found. He determined that black holes rotate at a constant rate so the size and shape of a black hole only rely on the mass and that rate of rotation. But because of that spin, a slight bulge would be near the equator and so it wouldn’t be a perfect sphere. And his work seemed to show all black holes eventually fall into a Kerr state (Hawking 91-2, Cooper-White).

In 1970 Brandon Carter took the first steps to prove that. He did, but for a specific case: if the star was initially spinning on its axis of symmetry and stationary, and in 1971 Hawking proved the axis of symmetry would indeed exist for the star was rotating and stationary. This all led to the no-hair theorem: that the initial object only impacts a black hole’s size and shape based off the, mass and rate or rotation (Hawking 92).

Not everyone agrees with the result. Thomas Sotiriou (International School for Advanced Studies in Italy) and his team found that if ‘scalar-tensor’ models of gravity are used instead of relativity found that if matter is present around a black hole, then scalars do form around it as it connects to the matter around it. This would be a new property to measure for a black hole and would violate the no-hair theorem. Scientists now need to find a test for this to see if such a property actually exists (Cooper-White).

## Hawking Radiation

Event horizons are a tricky topic, and Hawking wanted to know more about them. Take for example beams of light. What happens to them as it approaches the event horizon tangentially? Turns out, none of them will ever intersect with each other and will forever remain parallel! This is because if they were to strike one another, they would fall into the singularity and therefore violate what the event horizon is: A point of no return. This implies that the area of an event horizon must always be constant or increasing but never decreasing as time goes on, lest the rays hit each other (Hawking 99-100).

Alright, but what happens when black holes merge with each other? A new event horizon would result and would just be the size of the previous two combined, right? It could be, or it could be bigger, but not smaller than either of the previous ones. This is rather like entropy, which will end up increasing as time progresses. Plus, we cannot run the clock backwards and get back to a state we were once in. Thus, the area of the event horizon increases as entropy increases, right? That is what Jacob Bekenstein thought, but a problem arises. Entropy is a measure of disorder, and as a system collapses it radiates heat. That implied that if a relation between the area of the event horizon and entropy was real then black holes emit thermal radiation! (102, 104)

Hawking had a meeting in September 1973 with Yakov Zeldovich and Alexander Starobinksy to discuss the matter further. Not only do they find that the radiation is true but that quantum mechanics demands it if that black hole is rotating and in taking matter. And all the math pointed to an inverse relation between the mass and the temperature of the black hole. But what was the radiation that would cause a thermal change? (104-5)

Turns out, it was nothing…that is, a vacuum property of quantum mechanics. While many consider space to be primarily empty, it is far from it with gravity and electromagnetic waves traversing all the time. As you get closer to a place where no such field exists, then the uncertainty principle implies that quantum fluctuations will increase and create a pair of virtual particles which usually merge and cancel each other out just as fast as they are created. Each have opposite energy values which combine to give us zero, therefore obeying the conservation of energy (105-6).

Around a black hole, virtual particles are still being formed, but the negative energy ones fall into the event horizon and the positive energy companion flies off, denied the chance to recombine with its partner. That is the Hawking radiation scientists predicted, and it had a further implication. You see, the rest energy for a particle is mc^{2} where m is mass and c is the speed of light. And it can have a negative value, which means that as a negative energy virtual particle falls in, it removes some mass from the black hole. This leads to a shocking conclusion: black holes evaporate and will eventually disappear! (106-7)

## Black Hole Stability Conjecture

In an attempt to fully resolve the lingering questions of why relativity does what it does, scientists have to look to creative solutions. It centers around the black hole stability conjecture, otherwise known as what happens to a black hole after it has been shaken. It was first postulated by Yvonne Choquet in 1952. Conventional thought says space-time should shake around it with lesser and lesser oscillations until its original shape takes hold. Sounds reasonable, but working with the field equations to show this has been nothing short of challenging. The simplest space-time space we can think of is “flat, empty Minkowski space” and the stability of a black hole in this was proven true for it in 1993 by Klainerman and Christodoulou. This space was first to be shown to be true because tracking changes is easier than in the higher dimensional spaces. To add to the difficulty of the situation, *how* we measure the stability is an issue, for different coordinate systems are easier to work with than others. Some lead to nowhere while others *seem* to think they lead to nowhere because of a lack of clarity. But work is getting done on the issue. A partial proof for slow spinning black holes in de-Sitter space (acting like our expanding universe) has been found by Hintz and Vasy in 2016 (Hartnett “To Test”).

## The Final Parsec Problem

Black holes can grow by merging with each other. Sounds simple, so naturally the underlying mechanics are much more difficult than we think them to be. For stellar black holes, the two just have to get close and gravity takes it from there. But with supermassive black holes, theory shows that once they get to within a parsec, they slow down and stop, not actually completing the merger. This is because of energy bleed-through courtesy of the high density conditions around the black holes. Within the one parsec, enough material is present to essentially act like energy absorbing foam, forcing the supermassive black holes to instead orbit each other. Theory does predict that if a third black hole were to enter the mix then the gravitational flux could force the merger. Scientists are trying to test for this via gravitational wave signals or pulsar data but so far no dice as to if this theory is true or false (Klesman).

## Works Cited

Cooper-White, Macrina. “Black Holes May Have ‘Hair’ That Poses Challenge to Key Theory of Gravity, Physicists Say.” *Huffingtonpost.com*. Huffington Post, 01 Oct. 2013. Web. 02 Oct. 2018.

Hartnett, Kevin. “Mathematicians Disprove Conjecture Made to Save Black Holes.” *Quantamagazine.com*. Quanta, 03 Oct. 2018.

---. “To Test Einstein’s Equations, Poke a Black Hole.” *Quantamagazine.com*. Quanta, 08 Mar. 2018. Web. 02 Oct. 2018.

Hawking, Stephen. A Brief History of Time. New York: Bantam Publishing, 1988. Print. 88-9, 91-2, 99-100, 102, 104-7.

Klesman, Allison. "Are these supermassive black holes on a collision course?" *astronomy.com*. Kalmbach Publishing Co., 12 Jul. 2019.

**© 2019 Leonard Kelley**