# What happened when a black hole closed?

## Neutron Stars & Black Holes

• How do masses affect general relativity?
• How do black holes arise from the collapse of a star?
• What properties can be used to describe a black hole?
• How can black holes be observed?

Cover photo: ESO, ESA / Hubble, M. Kornmesser, (CC BY 4.0)

We recently discovered that neutron stars also have an upper mass limit, so they cannot be arbitrarily heavy. In order to understand what happens when the degeneracy pressure of the neutrons is no longer sufficient to stabilize the star, we need Einstein's general theory of relativity. More precisely, the theory of relativity is already necessary to understand details of white dwarfs and neutron stars that go beyond basic properties. But it is absolutely necessary for the black holes.

A key message of the General Relativity is that Crowds bend space. Now the space is three-dimensional, which is why it is difficult to imagine a curvature of it. You make do with it, for example, to depict it two-dimensionally like a cloth. A mass creates a dent in this cloth. Another variant shows the curvature by dividing the room with a grid, on which the effect of the mass can be seen.

General relativity predicts that masses bend space. Image: Alexander Gorfer (quant.uni-graz.at), (CC-BY-SA 4.0)

Free objects move on straight lines in empty space. However, if there is a mass nearby, it bends the space, as shown in the picture above. If an object moves past this mass, it feels the curvature of the room. We see that the object is distracted. We call this gravitational force. If one imagines this movement in the cloth analogy, then the movement of the object simply follows the deformed cloth. In classical mechanics and also in special relativity, gravity is not described in terms of the curvature of space. Both theories are borderline cases of general relativity for the case that you are only dealing with small masses that bend space only a little.

The general theory of relativity (right) predicts different orbits of the planets around the sun than Newton's theory of relativity (left). Only then could one explain the orbit of Mercury, where the closest point of the orbit to the sun "wanders" around the sun (perihelion). For more distant planets this effect is only minimal. Click on the picture for an animated version!
Image from: Simon Tyran (Yukterez), Orginal-GIF, (CC BY-SA 4.0) Other orbits

### what is a black hole?

A black hole is an area in which spacetime is so deformed and curved that neither matter nor light can escape from this area. The border between is called Event horizon, since an observer outside the black hole cannot hear anything from any event inside the black hole. That would only work if information reaches this observer in the form of light or matter.

If, in the case of a collapsing star, the degenerative pressure of the neutrons can no longer withstand gravity, a black hole is created. However, not every black hole has to be the result of a star collapse. For example, it is assumed that in the center of our galaxy (and other galaxies) there are extremely heavy black holes, the so-called supermassive black holes, with up to billions of solar masses. How such objects come about is, however, still an open question. There could also be another variant of black holes that were formed shortly after the Big Bang and that do not go back to the collapse of stars.

The idea of ​​a black hole was formulated even before the advent of general relativity. The escape speed of a mass \$ M \$ indicates how fast another mass \$ m \$ has to move in order to overcome the gravitational pull of \$ M \$. To do this, the kinetic energy is set equal to the potential energy and the escape speed \$ v \$ is calculated from this:

\$\$ \ frac {mv ^ 2} {2} = \ frac {GmM} {R} \ rightarrow v ^ 2 = \ frac {2GM} {R} \$\$

\$ G \$ is Newton's gravitational constant. Since nothing can move faster than the speed of light \$ c \$, one obtains a maximum escape speed \$ v_ \ text {max} = c \$. From this one can calculate the radius of the object of mass \$ M \$, at which the escape speed is equal to the speed of light. If the object is even smaller, nothing can escape its attraction:

\$\$ v _ {\ text {max}} ^ 2 = c ^ 2 = \ frac {2GM} {R_S} \ rightarrow R_S = \ frac {2GM} {c ^ 2} \$\$

\ (R_S \) is the so-called Schwarzschild radius. This calculation is not valid in the general theory of relativity and does not represent reality correctly either. It turns out, however, that the distance of the event horizon from the center of a black hole that does not rotate and is not charged is exactly the Schwarzschild radius.

### A black hole has no hair

A special property of a black hole is that it is completely described only by its mass, the amount of its angular momentum and its charge. A black hole contains no more information than this. So it is exactly described by these three properties. Of course, the position, speed and direction of the angular momentum are necessary to fully describe the black hole. However, these are all dependent on the choice of the reference system. In comparison, the position and all other properties of all (approx. 1057) Know particles that together make up the sun in order to describe them exactly. The fact that a black hole can only be described by these three numbers is called the "no-hair-theorem". The black hole has "no hair", so it does not carry any extra information with it. The current measurement data of the LIGO experiment seem to confirm this statement experimentally.

So if the black hole is fully described by these three numbers, where has the rest of the information gone, which was obviously still there when the star collapsed? After the formation of the black hole, these are either trapped behind the event horizon or were emitted in the form of gravitational waves.

By the way, a black hole is not an astronomical vacuum cleaner. It doesn't suck in matter until it's all gone. Otherwise we would not have existed for a long time. As with stars and planets, it is possible that other objects are in orbit around the black hole. The gravitation is only dependent on the mass. Nothing about that changes with the black hole.

### Observation of black holes

A black hole does not radiate and therefore cannot be observed using electromagnetic radiation such as light. But there are other ways of inferring the existence of black holes.

If there is gas around a black hole, it accelerates sharply before it crashes into the black hole. There is electromagnetic radiation from which observations can be made. Something similar can be observed when the black hole has a companion star and mass flows from it continuously into the black hole. The first system in which such behavior could be observed was the Cygnus X-1.

Mass flows from a companion star onto the black hole Cygnus X-1. Radiation is emitted, which can be used to detect the black hole (artist's impression). Image: NASA, ESA, Martin Kornmesser (ESA / Hubble) (CC BY 4.0)

### Gravitational lensing

In general, light always takes the shortest path between two points. In classical theory, the shortest path is a straight line. But this is no longer the case if the space is curved by a mass. So if you observe a ray of light near a large mass, you should see that it is following a curved path and no longer a straight line. It is similar to a lens that deflects a beam of light. This is known as Gravitational lensing.

Due to the gravitational lensing effect, an observer can see the same object several times.
Image: Alexander Gorfer (quant.uni-graz.at), (CC-BY-SA 4.0)

To a distant observer, light moves more slowly near a mass. This deflects the light rays from their path that they would take in a vacuum (left). This effect is called Shapiro delay and forms the basis of the gravitational lensing effect. Click on the picture for an animated version!
Image from: Simon Tyran (Yukterez), original GIF, (CC BY-SA 4.0) animation with other masses

The mass of an object can also be deduced from the gravitational lens effect. From an estimate of the mass and the size of the object, it can then be concluded whether the gravitational field is generated by a black hole. Another new possibility is that of gravitational wave astronomy. When the first gravitational waves were observed in 2016, it could be concluded from the type of signal that two black holes have merged. Gravitational wave astronomy is still at the beginning of its developmental stage.

In addition to observing black holes, the gravitational lensing effect is helpful in detecting Dark matter. In the early 20th century it was found that the rotation of spiral galaxies cannot be explained by visible matter. The outer areas of the galaxies rotate faster than calculated based on the observed matter. It is believed that dark matter is responsible for this phenomenon. This is matter that only (or almost only) interacts with the world via gravity - so we cannot observe it in any other way. What dark matter is made of is still a great mystery in physics. It is known, however, that there is apparently much more dark matter than visible matter in the universe. In addition to studying the rotation of the galaxies, the gravitational lensing effect is another indirect proof of dark matter, which allows conclusions to be drawn about the existence of dark matter in the universe, as one often sees greater effects than can be explained with visible matter. In addition, the gravitational lensing effect is used for many other purposes, such as distance measurements or the detection of neutron stars and brown dwarfs.

Dark matter could explain the rotational speeds of spiral galaxies. Here in the picture the galaxy Messier 81. Picture: NASA, ESA and the Hubble Heritage Team (STScI / AURA). Acknowledgment: A. Zezas and J. Huchra (Harvard-Smithsonian Center for Astrophysics) (CC BY 4.0)

There is more about dark matter in a separate article from the module "The Origin of Mass".