# Why does gravity create waves

Nobel Prize in Physics 2017 - Gravity waves

Klaas S. de Boer, Argelander Institute for Astronomy, Univ. Bonn

It happened in autumn 2015: gravity waves were detected for the first time. The scientists of the Laser Interferometer Gravitational-Wave Observatory (LIGO) took until February 2016 to do this world-wide. They wanted to be absolutely sure that everything was correct.

In order to understand how gravity waves were detected, some background knowledge should be explained. These are: 1.Gravity, space-time, potential well, 2. the most important thing about stellar evolution, especially with binary stars, and 3.Generation of gravity waves.

1. Gravity, space-time, potential well

Gravity waves are old. First, since the detected waves come from very far in the universe, they have come a long journey. But that comes later. Second, the idea of ​​gravity waves came from Einstein and the idea is now 100 years old. In 1916 he combined his theory of relativity from 1914 with an idea by Schwarzschild from 1916. Schwarzschild had thought about what the gravity field around a fictitious point mass (around a very compact star) would look like if Einstein's theory of relativity were included. Schwarzschild concluded that if the surface of a star (or any object) had very strong gravity, light cannot escape from its surface. Such an object should then be invisible. It would be a black point in the sky, as the light from the surroundings would also be drawn in by the strong gravity field.

When Einstein developed his general theory of relativity, he discovered a new way of describing gravity. He saw that it was not a force, as Sir Isaac Newton had postulated, but that Gravity is a consequence of the distortion of space and time, Space and time form a tight network, the "space-time". Objects distort the fabric of space-time because of their mass: heavy objects have a great effect.

If an object distorts space-time, how should we picture it? A mathematical description is easy if you know what you're doing. Graphically, one uses an analogy. Let's imagine an elastic plane on which a rectangular pattern is attached. An object on this plane will deform the plane due to its weight (gravity), the object creates a dent. The rectangular pattern is distorted, it is stretched towards the object. If we try to imagine this in 3 dimensions, it fails, we have no experience with 3-dimensional distortions. The analogy with a tarpaulin is a good one, however, it shows the object as a marble in its hollow. This led to the concept of the "gravity well", it is called the "potential well".

As everyone knows, when a marble is pushed towards a trough with sufficient speed, it can plunge into the trough and when it comes out it is usually in a different direction than the original one. If a marble circles around in a hollow, it stays there. In 3-dimensional space it all works in exactly the same way. The second drawing (not true to scale) shows how one can imagine the earth in the potential well of the sun. And of course, the earth has its own potential pot (as shown) in which the moon turns its orbits!

Now Einstein made a big leap. He said light doesn't go straight because gravity distracts it ... if you think classically. Seen from the point of view of the theory of relativity, light already has a straight path, but space-time is curved. So that, in classic terms, if you looked directly at the edge of the sun, you would have to find that the stars there would not be in their familiar position. This has now been confirmed during a solar eclipse. It made Einstein famous, even among outsiders.

All of this led to the following thought. Since a very heavy object has a very deep potential well (almost a pot with a hole in the bottom) so that light cannot escape, this object must appear black. Such an object became Black hole called. This name was later invented by Wheeler in the 1940s, but it became popular immediately.

 A black hole is an object in a very deep gravitational potential well, generated from a very compact object with a lot of mass, so that light cannot escape from this pot.
In order to be able to explain how black holes come about, something must first be said about stellar evolution.

2. Necessary for star evolution

Stars come in different sizes and they release different amounts of light. They develop according to their initial mass. Five simplified examples:
1. Stars with very little initial mass remain faint; at the end of their life they go out.
2. Stars with little mass (like the sun) develop towards a bright and short phase with great expansion, blowing away their outer layers and then shrinking into a compact "white dwarf".
3. Medium mass stars later become bright and expanded, they blow away part of the outer layers and then they explode, they become "supernova". A small, very dense "neutron star" is all that is left.
4. Stars with a large initial mass evolve quickly. When these explode and become a "supernova", a very compact and heavy one remains "Neutron star" back, which, if with enough mass, is also a black hole.
5. Many stars begin life as a pair, a "double star". They circle around each other in their overlapping potential pots. These stars are important for the creation of gravitational waves.

 Two nearby stars orbit each other in the common potential well. The curves under the pot show where the same gravity prevails in the pot. (Image © author). Two almost equally deep pots of potential. The star on the left is developing and expanding. Its outer gas layers flow over the saddle of the pot to the other star (picture © author).

Double stars orbit each other in a common potential well (picture; de ​​Boer + 2008). If they are close to each other, the overlap of the potential wells will strongly influence the development of the stars. If one of the stars expands and blows away outer layers, much (if not all) of this material will flow over the saddle of the pot to the other star, making the one more massive. Depending on both initial masses, this will lead to an interplay of mass exchange in the course of development. With each mass exchange, the development of each star is different, which means that modeling such systems is time-consuming. Two examples of the development of binary stars are given in the following figures.

There are innumerable variations in binary star systems. The stars will have different masses and their initial separation can be very different. Of course, closer couples will have more interaction. If both stars have a large initial mass, this system, after evolving with a lot of exchange of matter, can become a pair with one black hole, maybe even two, as in the example of Marchant et al. (2017).

 Simplified representation of the possible development of a binary star system. The numbers indicate the respective mass. Exchange of matter (by overfilling the respective potential pot) is indicated with arrows (picture © author). Developing a system with large masses. The end result is a pair of black holes that will merge. Names (ZAMS, TAMS, etc.) and mass of the stages are given, the number in the middle indicates the orbit period (see Marchant, Langer, et al., 2017).

One last fact is important. The stars orbit each other and exert a gravitational force on their mutual gases. This causes friction that is lost as heat, so that the system loses energy. As a result, the intermediate distance between the stars becomes smaller. A binary star system therefore gets closer over time, the two stars approach each other. However, if matter is lost to the system when the external gases are blown away, e.g. in a supernova explosion or in "polar jets" (see the heavy example; Marchant et al.), The orbit becomes more spacious and the orbit period longer.

3. Generation of gravitational waves

All waves propagate. Throwing a stone into a pond creates a wave at the point of impact.

 Waves caused by an almost stationary object spread outwards. When the object moves, the waves show an elongated pattern.
This wave propagates radially outwards, gradually becoming just a ripple of the water surface.

An object moving slightly on the water creates similar waves, except that the wave is higher in the direction of movement (than the opposite direction).
If two Objects moving around each other create an intricate wave pattern, with the individual patterns overlapping. And when such objects move quickly, the waves get higher and the spaces between them get smaller, the pattern looks very restless.

Now take the pattern of the potential well (see above) and let it rotate. This will generate waves in the space-time fabric. This is exactly what two black holes orbiting each other do.

 Simplified drawing of the waves created by two circling black holes in the space-time fabric. When two black holes circle towards each other, the waves get higher. Notice that the waves produced earlier are more diffuse. Image by LIGO.
An observer at a certain distance would feel this wave through the rhythmic expansion and contraction of space-time.

This was exactly the idea that Einstein had. The waves of gravity generated by two black holes that are inevitably circling each other very quickly will spread, the heights will decrease as the distance covered. Since the intermediate distance of the objects becomes smaller (because of the mutual friction loss), the orbit period becomes shorter, the wave rhythm faster, the speed of the objects greater, the objects become "circle", the generated wave is getting stronger ...

4. Detect gravity waves

Over the decades, scientists have considered whether gravity waves would ever be detectable. Their effects on the fabric of space-time would probably be minimal. But when lasers were developed, it immediately made sense to everyone to use them in an interferometry system for detection.

 The principle of the LIGO interferometer. A laser illuminates a mirror. Half of the bundle is reflected to the left through a semi-transparent mirror (indicated in green) to a second mirror, the other half goes straight ahead. Light from these two mirrors comes back, half is let through from the left, half is reflected from above to the right. These two bundles going to the right are combined and brought to "interference". 1 above In a well-aligned and calm situation (laser, mirror, other) the two bundles will reinforce each other. 2 below If a gravitational wave comes from the left (the yellow "wave"), the light path on the left is stretched and compressed, the path from above is not. This event creates a disturbance of the interference (picture from Wikipedia).

The first experiments were carried out at MIT in the 1970s. Other groups followed suit. Various research groups built prototypes for the detection of gravity waves with interferometry, including the GEO600 near Hanover (Germany). Ultimately, many groups cooperated to build the Laser Interferometer Gravitational-Wave Observatory (LIGO). The lasers for LIGO were manufactured at GEO600.

The principle of LIGO's functionality is explained in the picture. All elements of an interferometer must be positioned extremely carefully. Any disturbance (earthquake, storms, local traffic, ...) can destroy a stable interference. In addition, the light path from the laser to the mirror must be very long in order to be able to detect gravity waves at all. Therefore, the light bundles run through approximately 4 kilometers long closed tubes in deserted areas of the USA. The task of creating a stable position in two tubes at the same time .....

 The LIGO Station on the Hanford Reservation, Washington State, USA. Each tube protecting the light beam is 4 km long. On the right the pipe pointing north. Images from LIGO.

Two stations were built, one on the Hanford reservation in Washington State, the other near Livingston in Louisiana (see map; from Abbott + 2016). The tubes (arranged at right angles because of the interferometry) of these stations have a different orientation. This makes it possible to roughly determine the direction of origin of a gravitational wave. And with two stations, when both detect a wave, they confirm each other and it delivers twice the signal strength. Further LIGO stations are under construction.

And then it happened. LIGO, which was equipped with new laser systems from Hanover at the beginning of September 2015, was still in the test phase. All signals were also transmitted to Hanover immediately. On September 14, 2015 a wave hit, first in Livingston, only 7 milliseconds later in Hanford. In Hanover, the signal was recognized as possibly a gravitational wave. But it was deep night in the USA. You had to wait for the American partners to wake up. It soon became clear that the signals from Livingston and Hanford matched! Since the signals arrived with a time difference of only 7 ms, they must have come from the side of the Livingston-Hanford line.

The waves (the stretching and shrinking of space-time in the path of the laser light) show up as oscillations in the graphic (from Abbott + 2016). The difference of 7 msec in the arrival time is removed. The heights of the wave arrive at intervals of roughly 0.02 seconds. After that, the intervals get smaller and the amplitude increases, after which everything comes to rest. The whole thing lasted barely a second.

Modeling showed that this gravity wave came from an orbiting pair of black holes. The last figure shown here (by Abbott + 2016) shows the modeling of the event, in which one can see without "noise" what exactly was going on. The two black holes each had a diameter of about 200 km and a mass about 30 times that of the sun, both shortly before merging at about half the speed of light. From the weakness of the signal it could be deduced that the merger took place at a distance of a billion light years. The merging happened within 1/10 of a second.

Since then, three more gravity waves have been detected, one of them in the new VIRGO station in Europe.

The passage of a gravitational wave is something like a "space tremor", but with a timing opposite to that of an earthquake.

The 2017 Nobel Prize in Physics was awarded to LIGO's three long-time leading researchers: Barry Barish and Kip Thorne at Caltech and Rainer Weiss at MIT.

October 16, 2017: LIGO / VIRGO Merging neutron stars.

References.
- Abbott, B.P. et al. (LIGO Scientific Collaboration and Virgo Collaboration), 2016. Phys. Rev. Lett. 116, 061102.
- de Boer, K.S., Seghaben, W., 2008. "Stars and Stellar Evolution"; EdPSciences.
- Einstein, A., 1916. Meeting reports of the Royal Prussian Academy of Sciences. Berlin. part 1: 688-696.
- Marchant, P., Langer, N., et al., 2017. A&A 604, A55.
- Schwarzschild, K., 1916. Meeting reports of the Royal Prussian Academy of Sciences. Berlin; P.189ff.
- Wikipedia: https://en.wikipedia.org/wiki/Gravitational_wave

2017.10.14