Primary black holes

The origin of all black holes we know can be explained by astrophysical processes: the collapse of heavy stars and further growth due to their merger and falls substances (accretion) on them. But couldn't any black holes form in the first moments of the existence of the universe and even survive to our time? Such black holes are called primary. They have been talking about them for decades - this is a whole section of cosmology, so far suspended in the air. Primary black holes remain in the status of hypothetical objects, the real existence of which could have many interesting consequences in astrophysics.

In this article we will consider when and where they could appear and whether they are needed to explain modern data. This note is largely based on a review of the British astronomer Bernard Carr and German astrophysicism Florian Künel [ 1 ].

For starters, an important remark. Black holes evaporate through the radiation of hoking, and the smaller their mass, the faster they evaporate. This means that now only those black holes can exist, whose original mass was above 1015 g (1 km3 of water) - the easier have already evaporated. Moreover, the pace of evaporation grows with a decrease in mass, and the life of a black hole is proportional to the cube of mass. This means that now it would be unlikely to find a black hole now in the initial mass of 1015 g, and remain, say, 1014 g: they evaporate in one thousandth time of the life of the Universe. Therefore, we can safely assume that the vast majority of primary black holes in the modern universe (if any) are not easier than about 1015. Nevertheless, if such black holes were, their evaporation could affect the state of the early Universe so that this could lead to the observed consequences.

Another important remark: the mass of black holes formed at some point cannot exceed the mass contained in the volume of the horizon of the universe at the same moment. Such a mass grew over time: from the plank mass to a kilogram during inflation, then to the mass of the Earth in one nanosecond, then to the mass of the sun in ten microseconds, etc. (see Fig. 1).

Restrictions on the concentration of primary black holes?

The most popular “application” of primary black holes is dark matter. Indeed, they could well replace the hypothetical particles of an unknown nature, claiming the role of cold dark matter. Then it will not be necessary to look for new particles, but it will be necessary to invent the mechanisms of birth of primary black holes of the desired mass in sufficient quantities. Which of these possibilities is better consistent with the principle of Occam is difficult to say.

My personal opinion is new particles of the WIMP type (weakly interacting massive particles) - a less bulky new entity, although there is also an opposite point of view. Let us return to this issue in our final conclusions, and now we will determine F is the permitted share of primary black holes through the ratio of the density of their mass, averaged in space, to the density of dark matter. Recall that dark matter is about a quarter of the full density of the universe.

Dark matter from primary black holes as a whole fits into the observation data, if their mass lies in the range of 1017–1024 g - this is a typical mass of asteroids from several kilometers to several hundred kilometers in diameter. The primary black holes of the smaller mass at present would have been evaporated quite intensively, and then they would give either excess gamma-pon or too many positrons in space, which would contradict direct dimensions of the “voyage”. In addition, the annihilation gamma quanta 511 Kev from the center of the galaxy would be more than observed.

Why are the data of the Voyagers data used to limit the number of positrons when there are much more accurate data from closer spacecraft? The fact is that evaporating black holes weighing ~ 1017 g emit particles of energy hundreds of MeV - the positrons of such energy are unable to overcome the solar magnetic field and reach the particles detectors in the area of ​​the Earth's orbit.

Above the mass of 1024 g, gravitational microlysising comes into force. With such masses, the primary black holes would cause bursts of the brightness of distant stars, passing close to the ray of vision. Such an effect has long been observed, the number of weak objects in the galaxy, including freely walking (orphan) planets, is evaluated on it. With the help of microlynzing, even several dozens of ordinary (non -orphans) exoplanets were found. If all the dark matter consisted of black holes weighing above this limit, the frequency of microlysising events would exceed the observed one.

The most powerful restrictions on the mass of the black hole were obtained in the range of the masses of the lenses 1024–1027, they follow from observation of the stars of the M31 (Andromeda nebulae) using the Japanese Subaru telescope. The contribution of heavier black holes is limited by the observation of the stars of the large Magellanov clouds and the galactic bald (swelling). There is a weak place in this restriction: for the masses of the Earth’s mass, according to available data, it is possible to allow the contribution of primary black holes F up to 10%. Probably, with obtaining new data, this failure will close. In the mass range, slightly smaller than Mʘ (the mass of red dwarfs), the restriction imposed by gravitational wave detectors. If F exceeds 0.05 for the masses of the red dwarfs, then LIGO/Virgo detectors would find signals from their merger, which did not happen.

In the region of 1 mʘ and even more higher, this restriction does not work, since the merger of such objects is observed and for sure that they are due to neutron stars and ordinary black holes. Here F ~ 10-15%.

Further restrictions from observations of relict radiation come into force. If initially there were many black holes with a mass of more than dozen sunny, then in the period about 50 to hundreds of thousands from the beginning of the expansion of the Universe, the substance (accretion) actively pulled over to themselves, which would lead to a change in the temperature and degree of ionization of the early universe. This would contradict the "bar". The restriction on F reaches the level of 10–8 at m ~ 3 · 104 mʘ, for more severe black holes the limit is not calculated due to difficulties in assessing the pace of accretion, but other strong restrictions come into force there.

In the first second of the life of the universe, black holes weighing up to 105 mʘ, heavier - after, after when there was nucleosynthesis. They could have arisen from strong fluctuations in density, if there were such at that time, but these same fluctuations would affect nucleosynthesis so that this would contradict the observed primary chemical system of the Universe. But there is an even stronger effect. If, in times of tens of days to one hundred thousand years, strong fluctuations of density occurred that could lead to the appearance of black holes, then, despite the fact that the photons would subsequently diffuse and blur these fluctuations, the so-called entropy disturbances would remain, which would distort the spectrum of relict radiation (the so-called µ-Isk). This restriction is so strong that it limits the existence of primary black holes with masses from 105 to 1012 mʘ at a level that deprives them of any significant role in astrophysics.

Of course, this conclusion is made in the assumption that the distribution of fluctuations of density by amplitude is subject to the natural law of Gauss. And of course, theorists are trying to circumvent this restriction by inventing the Negasian fluctuations by complicating the theory of inflation or the invention of other mechanisms considered below. In such versions, long tails appear in the distribution of fluctuations in amplitude, which lead to a collapse of the medium into black holes.

As you can see, the primary black holes have a favorable range of masses - from small to the largest asteroids. Such black holes could well make up dark matter, remaining unnoticed. Moreover, they could successfully do the same as the “mainstream” dark matter from particles: to determine the dynamics of galaxies and their clusters, as well as play the role of cold dark matter in the early Universe. Another question is how to arise black holes of such a mass? It is considered below.

As for the other ranges of the masses, a certain number of primary black holes are still allowed to at least up to 105 mʘ.

Birth of primary black holes

Where could the primary black holes come from? In ancient work on this topic, it was assumed that they could arise when the density of the Universe was close to Plankovskaya. In that era, which lasted about 10–42 s (which is defended from the plank scale to one order), the quantum fluctuations of the space-time were so strong that any exotic in any amount could form: cosmic strings, magnetic monopolies, black holes, though small-with the mass of the one that was contained within the then horizon, which had the size of the size, which had the size of the size, which had the size About 10-32 cm. This is a gram of gram. Such black holes would instantly evaporate, perhaps the relics of the Planck mass of 10-5 g. But a little later, larger black holes could form from the cosmic strings.

It is unlikely that such an opportunity has something to do with our universe. The fact is that subsequently, probably, inflation, which had prompted all objects that could be born into the first moments, into gigantic distances, cleansing the space of all “near -plank garbage”. On the other hand, the inflation occurred at the density of the universe about 12 orders of magnitude lower than Plankovskaya (such a density was provided by the so -called inflaton), when the quantum fluctuations of the density are too small to give rise to black holes (nevertheless, these fluctuations led to the future to the birth of galaxies).

Can black holes be born during inflation? In ordinary space inflation models with Gaussian heterogeneities, such an opportunity is practically absent. Probably, some cunning models are possible where the nonsense is so strong that strong fluctuations appear that reach the collapse, but in any case, the mass of the black holes born is measured in maximum kilograms, and they quickly evaporate.

After inflation, the radiation-dominated stage begins, when the mass of matter in the volume of the horizon grows in proportion to the time. Accordingly, the mass of black holes is also growing that can form at this time: m ~ 1015 (t/10–23 c), that is, 10–23 seconds after the birth of the Universe, black holes can appear that can survive to our days. This requires much more relative disturbances in density than 10–5–10–4 arising from observations of relict radiation. At the radiation-dominated stage, which occurs immediately after inflation, in order for a certain volume (inside the horizon) to chop into a black hole, its density should exceed the average by about 45% [ 1 ], that is, 4 orders higher than the measured density dispersion.

If the amplitude of the disturbances is distributed according to Gauss (which is confirmed by the data of the “bar” and theoretical considerations for inflation models without “extracts”), then the scraping for 10,000 sigma is absolutely impossible. But we have data on the amplitude of the heterogeneities of the Environment of the Early Universe only in the interval of three orders of their size. And if in smaller heterogeneities, the traces of which are completely washed out, the dispersion of the density is much higher? The natural version of inflation excludes this - there all the disturbances arise as a quantum effect, with the same dispersion. Inflation itself makes indignation large-scale-invariant, and their distribution is only a little deformed when inflation is coming to an end. But is it possible to come up with such a model to sharply strengthen indignation in the area that cannot be observed? A lot of cosmologists work on this, and, of course, they have to use various tricks such as acoustic resonances that enhance outrage of a certain size. Otherwise, no black holes from the "classic" inflationary disturbances do not get density.

Is it possible to get primary holes in a different way, without contacting the primary disturbances of the density? There are several quite exotic opportunities associated with interesting moments in the evolution of the early universe. First of all, these are phase transitions, in particular the transition of Weinberg-Salam (splitting of electrical lace interactions into electromagnetic and weak), as well as the transformation of quarters and neutrons.

The first phase transition occurred during the order of nanosecond and could give black holes weighing about 1028 g, the second occurred at a mark of 10 ms and could give black holes comparable in mass with the sun. In order for this to be possible, it should be the first kind of transitions, when sharply falling pressure facilitates the collapse of disturbances with increased density. As an option, during phase transitions, bubbles of a new/old phase could occur, collide with each other and generate collapsing compression areas. Over time, it turned out that in both cases there was no phase transition of the first kind, rather there was the so -called crossover, when the system smoothly moved from one state to another, bypassing a critical point on the phase diagram on top.

Even earlier, in addition to these two well -known phase transitions, something interesting could happen - for example, unknown heavy particles could be born. If they lived long enough to become dominant as the Universe cools, then the pressure again falls and the conditions for the collapse of heterogeneity arose, which was shown by Astrophysicists by A. Polonarev and M. Khlopov in 1982. True, no hints of the existence of such particles have yet been discovered.

Finally, it is worth mentioning another exotic opportunity: the existence in the early universe of the scalar field with a bario charge. The heterogeneity of such a field at a certain stage could lead to a severe violation of the baronic symmetry-somewhere there are a lot of baryons, somewhere anti-Barions, when cooling, such clouds could collapse. Such a version of the development of events is developed by an astrophysicist from ITEF Alexander Dolgov.

Early heavy quasars

Perhaps the most urgent application of primary black holes is the early quasars (ultra -massive black holes). The problem of the early Quasars has already been considered in the publication of a TRV-hobby [ 2 ]. There is a restriction on the growth rate of black holes associated with the fact that the radiation distinguished by the falling substance is stopped by the fall on distant approaches. Hence the limit to the luminosity of the gravitating object, which is called the Eddington limit. It is proportional to the mass of the object.

The higher the rate of accretion of the black hole, the greater the luminosity, therefore, the appropriate restriction, also called Eddingonovsky, acts at the pace of accretion. This, in turn, means that the growth rate of a black hole is limited. At the same time, in the first about 700 million years in the universe there were already quasars with a mass of order of a billion solar masses. In order for them to form, at the start, at the time of tens of millions of years, black holes are already about 105 mʘ. There is a temptation to attribute them to the primary black holes. These were supposed to form somewhere during nucleosynthesis, they have quite strong restrictions, but there are not a lot of them-early heavy quasars are quite rare.

A huge number of articles are devoted to this problem. Of course, there are hypotheses that are not associated with the existence of primary (i.e., in this case, the era of nucleosynthesis) of black holes. Enough massive copies could occur in the first tens of millions of years, bypassing accretion. For example, by hierarchical fusion of black holes remaining from the first very massive stars. This could well have taken place in dense stars. There is another scenario - a direct collapse of gas clouds with stars weighing millions of solar masses. Such clouds were just thickened in the first tens of millions of years. But these models have its own problems: how to devote the heat released during compression? However, the scientist finds outs . Another option is a mode with very low radiation efficiency, when the substance falls, almost nothing emitting out, and all the released energy is carried into the black hole. Thus, the limitation on growth rate is greatly weakened. So far, there is no complete clarity with these capabilities, but in any case, the accompanying problems are clearly no more complicated than those that are associated with the hypothetical birth of black holes of the desired mass.

Conclusion

In general, the author’s position of this note regarding any significant role of primary black holes in cosmology is quite skeptical. There are no direct strong arguments for this skepticism, there is rather indirect: the principle of Occam. Первичные черные дыры требуют лишних сущностей, причем довольно радикальных, не будучи жизненно необходимыми для объяснения наблюдений. Тем не менее этот скептицизм не распространяется на людей, которые ими занимаются. Так уж устроена наука, что исследоваться должны любые возможности. Это просто интересно и развивает совокупный интеллект человечества.

К тому же есть одно важное замечание, высказанное в частной беседе Александром Полнаревым: если вдруг обнаружатся следы черных дыр массой порядка масс астероидов, это будет единственным «приветом», который может долететь до нас из самых ранних времен до фазового перехода Вайнберга — Салама, из Великой энергетической пустыни, недоступной изучению на ускорителях. К тому же, если в те времена лишь ничтожная часть плотности энергии перешла в черные дыры, то по мере остывания Вселенной их доля возрастет на несколько порядков величины (их масса не уменьшается, а плотность энергии среды падает на порядки). В это верится с трудом, но все-таки, а вдруг! Но даже из отсутствия первичных черных дыр, по мнению А. Полнарева, можно получить немало интересной информации о физике самой ранней Вселенной.

Boris Stern

1. Carr B., Kuhnel F. Primordial Black Holes as Dark Matter: Recent Developments . arXiv:2006.02838v3

2. TRV-SCIENCE.ru/2021/02/OTKUDA-VZYALIS-MOSHHNYE-RANNIE-KVAZARY