3.1. Parameters of terrestrial black holes
3.2. Problems of accretion onto small black holes and fermi-otons.
3.3. Gravitationally-connected systems of fermi-otons (grassifotons).

The opinion that black holes, being in the Earth, must easily manifest themselves dissipates by first rough estimations of effects caused by them. Even if there are billions of small black holes in the Earth their finding is too hard, since their gravitational fields merge with that of the Earth.

The gravitational radius of the Earth is few less than a santimeter. Black holes of smaller masses possess microscopic sizes and they move freely through the Earth. Their manifestations are rather considerable but very localized. For example, a black hole with the mass of large city has the size of an atomic nucleus. If it appears in the centre of ordinary table, the black hole gravitational force at a distance about one santimeter from it will be ten thousands times greater than the earthly gravitation. Outside the table the black hole gravitation will not be almost felt.

Among otons of small masses the so called micro-black holes have been investigated better, though the name of these objects is incorrect by several reasons. The first, these objects are not black, since due to the Hawking effect they shine and "become white-hot". The second, masses (respectively, sizes) of these objects decrease because of the Hawking evaporation, i.e., the black hole is compressed and disappears. Hence, these objects are not black and in course of time they cease to be holes. Therefor in many cases use is made of the term "otons", which has no such inconsistencies.

Micro-white holes can appear to be stable, because their behaviour must be quite opposite to that of evaporating and exploding black holes. Thereby, the less investigated case of micro-white holes, some parameters of which coincide with those of terrestrial black holes, is of interest for geophysics of otons. Let us characterize in short parameters of terrestrial otons.  

Table 3.1.1.

 

 

3.1. Parameters of terrestrial black holes (to the top). We shall present first sizes of black holes possessing masses of solar system objects (the Earth, the Moon and planets). In this case for determining the gravitational radiuses the following formula is convenient:

 

R_g (sm) = 1,484  10^-28 Ì (g) = 0,887Ì (M _Å ).                    (3.1.1.)  

 

As it is evident from (3.1.1.) the mass of all the objects of our planetary system (besides of the Jupiter and the Sun), being concentrated in black holes, would be allocated in one room, and a black hole with the mass of the Earth (M _Å ) in one dove egg would.

Masses and sizes of terrestrial black holes (BH) in comparison with objects of micro-world and terrestrial bodies are submited in Table 3.1.1. In first two columns the black hole masses, multiple to ten, and the corresponding gravitational radiuses are presented. In the third and fourth columns are the gravitational radiuses, multiple to ten, and the corresponding black hole masses.

A black hole of a mass M has the density:

 

 =  (g/sm³),     (3.1.2.)

 

which decrease in inverse proportion to mass square.

A black hole with a mass of the Earth has density  10²⁷ g/sm³, which is in twelve orders more than that of nuclear substance. A black hole with the mass of a person ( g)  has the radius  sm, which is in ten orders less than that of elementary particles, and its density is equal to  10⁷¹ g/sm³.

According to the expression (3.1.2.) the less black hole mass, the more density of its substance. If the whole Earth's mass be concentrated not in one, but in N black holes, the total volume of all black holes would be equal to:

 

                                        V_NBH = N^-2V_BH ,                                 (3.1.3.).

 

where V_BH is the volume of the black hole with the mass of the Earth; V_NBH is the total volume of N black holes, which the total mass is equal to the mass of the Earth. Linear "sizes" R_NBH of this total volume is equal to:

 

                                        R_NBH  = N^-2/3 R_BH ,                             (3.1.4.).

 

where R_BH is the gravitational radius of the Earth. If the whole Earth's mass was concentrated not in one, but in billions of black holes, the total volume would sharply decrease and would equal to the volume of one molecule. The total volume of all the terrestrial black holes is rather even less value.

Already this brightly shows, so far as the task of finding objects, the total volume of which in the Earth does not exceed the molecule volume and is in fourty four orders less than the volume of the Earth itself, is difficult. Nevertheless, gravitational fields of terrestrial otons allow the direct gravimetric registration of black holes.

For imagining clearly gravitational manifestations of otons on the Earth it is necessary to determine the gravitational force acceleration (g_BH) caused by black holes of different masses (M_BH) at different distances (R_BH) in comparison with that at the Earth's surface (g). This condition gives:

 

                                      ^-2 = M_BH R_BH ^{-2 .}                        (3.1.4.).

 

For convenience of estimations let us enter the basic values of M_BH and R_BH: R_BH = R₁ = 1 sm; М _BH = M₁ = 1,47310¹⁰ g.Taking account of these values the mass of the black hole, which causes the acceleration (g_BH = g) at distances, multiple to 1 sm, is easely determined by the formula:

 

                               М _BH   =  (R_BH/R₁)² M₁ .                                (3.1.5.).

 

For determining distances (R_BH), at which black holes with masses multiple to 10¹⁰ g cause the acceleration g_BH = g, another set of basic values M_BH and R_BH is convenient: М _BH = М ₀ = 10¹⁰ g;  R_BH = R₀ = 0,824 sm,and so is the next expression:

 

                               R_BH = (M_BH/M_o)^{1 /2}R_o.                                    (3.1.6.).

 

At last, the formula, defining the distance R_k, at which g_BH = kg, when the mass of black hole M_BH is given, is useful:

 

                                        R_k = (k)^-1/2 R_BH.                                 (3.1.7.).

 

The gravitational force of the black hole with the mass of 1,47 × 10²⁰ g at the distance 1 km will be equal to that of the Earth, at the distance 1 m it excceeds the later millions times, and so does it thousands billion times at the distance 1 mm. One can imagin, what giant tornado such the black hole would cause, if it appeared near the terrestrial surface. The above testifies the variety of terrestrial black hole manifestations in dependence on their masses. Black hole interaction with matter else more varies black hole manifestations.

3.2. Problem of accretion onto small black holes and fermi-otons (to the top). Not only the quantum evaporation of black holes, but the accretion of matter can be a source of terrestrial black hole energy. Due to some reasons the question on accretion of hard substance of the terrestrial corex onto black hole is problematic. For example, the hard substance being in the connected state, the preliminary work for its destruction is needed. Therefore, in black hole's passing through the terrestrial matter the tracks (cords, through apertures) must be formed.

However, the main problem of the terrestrial black hole existence is connected with the rapid accretional absorption ("devouring") of the space body by the black hole. But objections available concerning accretion does not take account of quantum nature of the region, in which the accretion onto small black holes occurs. In accrueing matter onto small black hole a fermi-system must be formed, which plays the role of a source of repulsion. The task of accretion of degenerated fermi-system substance onto small black hole not only was decided, but even seem was not put.

Only those particles of fermi-system will accrue, the velocities of which are less or equal to the rate of black hole seizing. Those are the particles to be "at the bottom of fermi-system particle energy distribution". It means that the particles of fermi-system come away in the black hole not with maximal velocities, but with minimal ones. The situation is quite opposite to ordinary "evaporation" of particles with maximal velocities. The minimal mass (M_min), which can accrue onto small black hole, is defined by the sum of all the particles possessing velocities.

Neutron stars and white dwarves stabilize the degenerated substance by their own gravitational field, but if the masses are less than some critical value, the gravitational field is turned out too weak for stabilizing the fermi-system. Possessing the considerable intensity of gravitational field small black holes can create large gradients of pressure and form fermi-systems of smaller masses. It means that there happens the stabilizing of fermi-otonic system by the black hole gravitational field resulting in fermi-oton formation.

The bottom limit for masses of such systems is connected with the Hawking effect, and those masses can not be less than 10⁶ kg, because of exploding of those small black holes. Though, it should be noted that the Hawking effect in a substance must be essentially modified, therefore the bottom limit for fermi-oton mass can be lower considerably.

The structure of fermi-otons must be qualitatively similar to the structure of degenerated stars: shells with different material contents and densities decreasing to the surface will lay from the centre to the surface. As far as fermi-otons are concerned the neutrinic shell is of especial interest, since it is transparent for a substance, does not make a "friction" in the Earth and is not teared by the terrestrial matter.

In a case of small black hole exiting from a fermi-system (for example, the retardation of a fermi-oton in a dense environment should lead to appearing the differance between the velocity of oton motion and that of surrrounding substance) a fermi-system must decay forming transuranium elements. Thus, deposits of transuranium elements are places of fermi-oton decays. Possessing the strong magnetic field like neutron stars, fermi-otons can cause short-term variations of the terrestrial magnetic field, i.e., the correlations between gravitational potential derivative variations and variations of the magnetic field should take place.

Let us pay attention to nuclearities, i.e., objects, which are nearest by their properties and manifestations to fermi-otons. E.Witten has pointed out the possibility of nuclear substance, which consists of white, black, and strange quarks compounding it, to be less massive than usual nuclear matter with the same number of quarks in proton and neutron compounds. These clots of the strange quark matter can be stable for almost all barionic numbers (A), including those in interval between ordinary nuclei (A £ 263) and neutron stars (A » 10⁵⁷).

A.De Rujula and S.L.Glashow, having introduced the term "nuclearities" for these objects, discribed the properties of such quark formations, the probability of their meeeting with the Earth and presumable experiments for detecting such meetings. According to the authors, nuclearities can manifest themselves on the Earth as meteors, as etched routes in mica and mountain breeds, they can create astroblems and cause earthquakes. All these phenomena can be caused by fermi-otons as well, but with one essential clause: one must take account of though localized but very strong gravitational fields of otons.

Summing up it is possible to say, that real terrestrial black holes can not be single and "naked", and the substance, gravitationally connected with them, makes otonic manifestations more various. Models of gravitationally connected fermi-oton systems have more wide heuristic opportunities.

3.3. Gravitationally connected systems of fermi-otons (grassifotons) (to the top). Let us notice, that it is more correct to speak not about systems of "naked' single otons, but about gravitationally connected systems of fermi-otons (GCSFO). It means objects with different states of matter, which has different densities and temperatures, to be in a close neighbourhood. It tells not only about real GCSFO discription difficulties, but about the large heuristic potential of these objects in physics of the Earth. Different geophysical phenomena can be attributed to an action of GCSFO, which have parameters required. For these objects taking account of their reduced name it is possible to introduce the terms "grassifotons" or " grasfoton systems".

GCSFO can be verious, e.g., multiple systems, systems of planetary type, systems of otonic gas type and others. In this section estimations of characteristic parameters of such systems (system sizes, a velocity and a period of oton-sattelites rotation around the attractive centre, parameters of gravitationally connected system motion on circle orbits around the centre of the Earth), which are in the gravitational field of the Earth, as well as in the absence of the external gravitational field, are considered.

The estimations of some GCSFO parameters were given in the joint with O.L.Artemenko work [Òð51]. The analysis of the given estimated results shows, that the meaning for the otons- satellites is insignificant. The analysis of estimation results presented there shows the value of R₀^* for otons-satellites to be not large. So, in M₀^* changing from 10¹¹ to 10²¹ kg R₀^* is changed from 0,825 to 83516 m. The velocity of oton-satellite motion on circle orbits around the attractive centre is small too, which is conditioned by small (compared with M _Å ) masses of attractive otons. For example, the velosity of motion of an oton with the mass M₀ = 10⁸ kg (pre-explosive oton) on the circle orbit around the centre with M₀^* = 10¹¹ kg is equal to 2,85 m/s, while the period of satellite rotation is equal to T₀^* = 1,82 s.

In free GCSFO, where an external gravitational field does not restrict system sizes, otons-satellites can located both on orbits with radiuses R < R₀^*, and on those with R > R₀^*. In the case given the velocity V₀^* decreases, when the circle orbit radius increase, but the period of rotation T₀^* grows. For example, in the case of an oton-satellite with the mass of 10⁹ kg the velocity and the period of rotation on the circle orbit with the radius R = 100 R₀^* around the centre with M₀^* = 10¹³ kg will be equal to 0,9 m/s and 918 s (15,3 min) accordingly.

Systems with sizes 100R₀^* and more (i.e. with R > R₁) can not actually exist, since GCSFO in this case turn out to be unstable, and a re-seizure of otons-satellites by internal masses of the Earth is possible. As a whole, a sufficiently large number of otons-satellites, locating on internal orbits with R £ R₁ and moving with small velocities,  can rotate around the central oton. Such the system reminds the ordinary planetary system such as the Solar one. The presence of a large number of otons-satellites on internal orbits will lead to periodical changes of their parameters due to mutual satellite's influences upon each other.

As concerned with the possibility of the existence of GCSFO an attention should be payed on the universal empirical fact, that is: all known gravitational objects enter in those or others gravitationally connected systems. The only question is so far these systems are close. It seems obvious due to universality of the low of gravitational attraction. Thereafter, there are no any grounds to make such conclusions in respect of small black holes. Not the existence of GCSFO, but of single black holes, requires the substantiation.

All types of GCSFO regarded (excluding systems with the radius of oton-satellite orbit about 1 km or more, when the action of the centre and that of otons-satellites is separable) will not considerably differ from single otons by their gravitational manifestations. Otons-satellites will contribute additionally in total energetics of the system. An explosion of one oton of the system does not mean the cancellation of system acting as a whole (if, for example, one consider GCSFO supplying the volcanic activity in a certain region), since other otons of the system will go on extracting energy. This example shows the qualitative difference of GCSFO from single otons: an explosion and a termination of existence of a micro-black hole does not mean a termination of energetics manifestations of GCSFO.

Grassifotons of different types can exist in the Earth: from macro-grassifotons up to micro-grassifotons. Macro-grassifotons are characterized by sizes from 10^-1 to 10⁶ m and small rates of oton-satellite rotation on circle orbits. Actual sizes of a macro-system in the Earth can be estimated on the basis of the data on all system oton masses and on the radius of the connected system orbit relative to the centre of the Earth. Micro-grassifotons are characterized by sizes from 10^-7 to 10¹ m, rather large velocities (which attain the first cosmic one) and small periods of oton-satellite rotation.

In regarding many tasks it is possible to neglect various properties of grassifotons and regard them as micro-objects with a large gravitational mass (as point masses). So, analysing grassifoton motions in the Earth they can be regarded in the first approximation as single, and "naked", black holes.