# Einstein’s space-time configuration is not stable: a small piece of matter can form a black hole

BEIJING, May 19 (Xinhua) — According tomedia reports, Einstein’s equations describe three typical configurations of space-time. Now, scientists have shown that one of the configurations that is important in quantum gravity research is inherently unstable.

From 2017 to today, mathematicians have shown in a series of work that einstein space-time configurations called anti-de Sitter space are unstable. If a small piece of matter is thrown into AdS space, a black hole will eventually appear. This mechanism can also be applied to other situations unrelated to AdS, i.e. matter or energy is enclosed in a physical system that does not escape from the exit.

Although we do not live in an anti-Deset universe (if we do, we would not exist), this study is important for us in understanding the mysterious link between gravitational theory and quantum mechanics.

The expansion of gravity

The uncertainty hypothesis – and the resulting entire school of thought – can be traced back to Einstein’s general theory equation of relativity, which accurately illustrates how mass and energy affect the curvature of space-time. There is no matter in the vacuum, but because of the energy density of the vacuum itself (described as the “cosmic constant”), space-time is still curved and gravity remains. As it turns out, the vacuum is not empty at all.

The three simplest solutions to Einstein’s vacuum equation are the most symmetrical, with the same instant alpaca everywhere. In the time and space of The Yinkovsky, the universe is zero and the universe is completely flat. In the Desit sky, the cosmic constant has a positive value, and the universe is shaped like a sphere. When the cosmic constant is negative, you get AdS space-time, which is saddle-shaped. In the early days of cosmology, scientists wanted to know which of these three timespaces described our universe.

Mathematicians, on the other hand, tend to wonder whether these space-time symms are really stable. In other words, if you disrupt vacuum space-time in any way (such as injecting some material into the system or sending some gravitational waves), will it eventually return to its original state? Or will it evolve into something completely different? Is it like throwing a stone into a cosmic “pond” and the waves will gradually decrease, or will they gradually form a tsunami?

In 1986, a mathematician proved that Desit time and space were stable. In 1993, two mathematicians came to the same conclusion in their study of Yukovsky’s space-time. Research on the AdS problem took longer. The general consensus is that, unlike the other two configurations, AdS is unstable, meaning mathematicians will have to adopt a completely new approach. Researchers have developed a number of mathematical tools to solve stability problems, but instability is a completely different area — especially this type of instability. In essence, this instability is nonlinear, resulting in inherent complexity and more complex calculations.

The researchers suspect that the instability of AdS space-time may be due to its boundary reflecting, causing it to “look like a mirror, and any wave that hits it will reflect back.” From a physical point of view, reflections on boundaries make sense, possibly because of the curvature of the AdS space, but there is a simpler explanation: the principle of energy conservation.

If the boundary is essentially reflective, then nothing can escape from the Air time of AdS. As a result, any matter or energy entering the system is likely to gather, or even to the extent to which a black hole forms. The question is, is this really going to happen? If so, what mechanisms cause matter and energy to gather to such a degree rather than be dispersed?

You can imagine yourself standing in the middle of AdS time and space, like standing in a giant ball, with the edge or boundary in infinity. If a light signal is sent from there, it will reach the boundary in a limited time. This propagation is possible because of a well-known relativistic effect: while the spatial distance to the boundary is indeed infinite, time is slower for waves or objects moving at or near the speed of light. Thus, observers standing in the center of AdS space-time will see a beam of light reaching the boundary for a limited time (which requires some patience).

If we don’t use light, we put a substance commonly used in general relativistic models, the Einstein-Vlasov particles, into AdS space. These particles produce concentric waves of matter in the air at times, similar to water waves that occur in ponds.

When matter suddenly enters this space-time, there are many concentric waves, the first two of which will be the largest. These two waves contain the most matter and energy, so we will focus on them. The first wave, called “wave 1,” expands outwards until it reaches the boundary, then bounces back and shrinks the waveform as it returns to the center. The second wave, Wave 2, will follow Wave 1.

When Wave 1 bounces from the boundary and begins to shrink toward the center, it hits Wave 2, which is still expanding. Mochidis is convinced that one of the results of Einstein’s equation is that in such interactions, the expansion wave (wave 2 here) always passes energy to the contraction wave (wave 1).

Once Wave 1 reaches the center, it will start to expand again, and meet Wave 2, which is shrinking at this time. This time, Wave 1 will pass energy to Wave 2. This cycle can be repeated many times.

The closer you get to the center, the less space the waves take up, the more concentrated the energy they carry. Because of this, waves exchange more energy in the interaction near the center than in the interaction near the boundary. The end result is that wave 1 gives wave 2 more energy in the center than wave 2 gives wave 1 at the boundary.

After numerous repetitions, Wave 2 becomes larger and larger, constantly absorbing energy from Wave 1. As a result, the energy density of wave 2 continues to accumulate. At some point, when wave 2 shrinks toward the center, its energy becomes very concentrated, creating a black hole.

This is evidence of instability. When a very small amount of matter is added to the AdS time-to-air, a black hole (or more black holes) will inevitably form. By definition, however, AdS space-time has uniform curvature everywhere, which means it cannot accommodate objects that distort space like a black hole. If you disrupt AdS space-time and wait long enough, you end up with a different geometry that will contain a black hole, which is no longer AdS space-time. This is what we call instability.

Not long ago, mathematicians demonstrated AdS instability through another material disturbance, the so-called mass scalar field. Since the waves produced by the scale field can be considered as substitutes for gravitational waves, it is a step closer to proving AdS instability in a real vacuum. In a true vacuum, space-time is only severely disturbed by gravity without the introduction of any matter.

AdS Space and Turbulence

The instability of AdS space-time has a significant impact on how we understand the universe in which we live. First, because AdS space-time is unstable, “you don’t see anything like that in nature.”

But even if AdS is not real, it can still lead us to discover and study the real phenomenon. For example, when energy is concentrated from a large scale to a small scale, “turbulence” occurs, and turbulence occurs when AdS space-time is disturbed. However, turbulence is a phenomenon that is widely present in various fluid systems, and little is known about it. AdS space-time is a “clean” and relatively simple system, which is why AdS is a “good theoretical testing table” for studying turbulence. In the setting of AdS space-time, turbulence is caused by gravity, but mathematical tools being developed can also help to analyze turbulence in fluid mechanics.

AdS also plays a prominent role in the so-called “AdS/CFT pair” (all known as anti-Desit/co-form field pairing), which is a key clue to the integration of quantum mechanics and gravity in an all-encompassing theory of quantum gravity. This pair shows that the gravitational system in AdS space can be equivalent to a non-gravitational quantum system with one less dimension. We can describe it in a quantum mechanical system that does not contain gravity, not by the theory of gravity, the theory of gravity in the AdS universe, rather than the theory of gravity in our universe.

The new findings, combined with AdS/CFT pairing, could also help shed light on the more familiar areas of particle interaction. For example, the tiny disturbances of AdS space-time are used to create black holes, a process that, by coupling, is associated with the thermoization process that causes quantum systems to reach equilibrium, an almost universal real-world phenomenon.

Proving that AdS is unstable doesn’t mean it’s becoming boring. (Any day)