Black rings explained

08-BlackRing

Most people have heard of black holes before, and at least understand its idea. But not many have even heard about black rings. As was mentioned in an earlier post, the black ring is one of many types of black holes that most people haven’t heard about. One of the most recent and significant discoveries is the five-dimensional black ring. Discovered by Roberto Emparan and Harvey Reall in 2002, it sparked a new wave of interest in the research of General Relativity, which, during that time, was considered to be a well-matured (i.e., old) field of study.

It is true that in four dimensions (4 dimensions=3d space+ 1 time), General Relativity (GR) is a pretty well-matured field of study. The no-hair theorems establish that the only kind of black hole that can exist is precisely described by the Kerr black hole. That is, if I am given any pair of numbers describing an object’s mass and rotation, I can write down the exact equations that determine exactly the nature that black hole using the Kerr metric.

This amazing precision is not shared by ordinary planets. Earth and Venus have nearly the same mass. We can imagine taking away chunks of Earth so that its mass would match exactly that of Venus, but they are undeniably different planets. Their atmospheres differ, they have different geology and surface structures, among other things.

This is the reason why it’s called the `no-hair’ theorem. A bunch of bald-headed people look almost identical, while it’s much easier to tell people apart in a group of people with differing funky hairstyles. Black holes have no hair. In four dimensions, all black holes are essentially deformed spheres. The faster it spins, the more deformed the sphere.

When Roberto Emparan and Harvey Reall studied relativity in five dimensions in 2002, they discovered a new type of black hole that violates this theorem! They started by first considering static (non-rotating) black holes, and extending an old method (Weyl metrics) into higher dimensions

01-generalised.weyl.png

This is the paper where they found the static black ring (a publicly available pre-print can be found here). The static black ring, however, is unstable. Since black holes are gravitating objects, its own gravity will cause the ring to collapse into a spherical black hole again. In order for the static ring to be constructed, one needs to hypothetically place a solid disc within the ring to hold it from collapsing. In technical terms, this is called a conical singularity. This highly contrived situation is, of course, not very interesting physics.

What if the black ring is spinning? As we know from everyday life, things going in a circle will feel an outward force. When a car goes really fast in a roundabout, its passengers gets thrown to the side that faces away from the roundabout. This is called centrifugal force. In their next paper, Emparan and Real derived a solution describing a rotating black ring, where its centrifugal rotation balances itself from gravitational collapse. Thus there is no more conical singularities inside the ring, and we have what physicists call a regular solution.

02-BR.PRL.png

The publicly available preprint for this paper is here.

I mentioned earlier that if we know the specific mass and angular momentum of a black hole, we can identify it exactly using the Kerr metric in four dimensions. However in five dimensions, with the discovery of black rings it is no longer possible.

03-phase.diagram.png
[image from hep-th/0608012]

Emparan and Reall calculated the range of possible surface area (which depends on mass) and angular momentum of the black hole. And in the above phase diagram, for the range of j^2 between \frac{27}{32}\leq j^2\leq 1, we see there are three possible black holes – `fat’ and `thin’ black rings, or the Myers-Perry (MP) black hole. Thus the no-hair theorem is violated!

This momentous discovery by Emparan and Reall breathed new life into the research of classical General Relativity. Many physicists followed up with many of their own results and analysis of the black ring and attempted to find more solutions in five and higher dimensions. Such groundbreaking work only happens very occasionally in physics. And even more rarely in such an old theory such as General Relativity.

 

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