6. Some issues on terrestrial black hole radiation

6.1. Laws of black hole physics and the problem "of thermal death" of the Universe.
6.2. Neutrino radiation of small black holes.
6.3. Explosions of black holes. Plankian particles. Theories of the Great Unification.
6.4. Relativistic geological petroleum exploring and thermonuclear reactions in the terrestrial interiors.

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6.1. Laws of black hole physics and the problem "of thermal death" of the Universe (to the top). In investigating black holes their laws were found out to be similar to the principles of thermodynamics. Let us make a small deviation, having looked into the most interesting problem "of thermal death" of the Universe, which is connected with the principles of thermodynamics.

Black holes have one property essentially distinguishing them from classical astrophysical objects: they only absorb radiation and substance. This property of black holes has found a reflection in the so called Hawking theorem, who has proved the area of black holes not to decrease in any classical interactions of them with each other and with the environment.

Due to S.Hawking, J.Beckenstein and other scientists works the laws of black hole physics were formulated, coinciding by the form of mathematical record with the laws of thermodynamics [Be10], [Ha01,3], [Õî01,2,3], [Øÿ00], [Ôð00,1].

Equivalents of thermodynamic quantities, i.e., entropy and temperature, in black hole physics are accordingly the area of surface and the superficial gravitation. Decrease of temperature or increase of entropy of black hole corresponds to increasing of its mass, i.e., not dispersion, but concentration of matter is connected with increase of entropy.

Thus, the laws of black hole physics are connected with the irreversible nature of space substance and radiation concentration. For the first time in science there were predicted and discovered objects which can resist to thermodynamic processes of energy dissipation. In the future stellar objects and space systems must finish their evolution by black hole formation. In the course of time the era of domination of processes of dissipation of radiation and energy must be changed by the era of their concentration.

Mutual transformations of forms of motion and energy in space can be presented as follows [Òð00,8]. The energy of radiation, dissipated in initial STM (otonic world) Ì (0, +) (see Fig.1.4.1.) and concentrating in STM of black holes M (0, i), transforms in kinetic energy of motion. Collapse of oton matter in the region Ì (0, · -) turns into anticollapse. A sort of oton matter recoil occurs: compression is replaced by repulsion. Then the kinetic energy of matter dissipated by a white hole in regions M (1, -i), M (i, +) transforms into the gravitational potential energy.

The fragmentation of substance dissipated in another otonic world Ì (1, +) leads to the transition of potential energy in thermal. This process, growing, results in formation of star objects, in which thermal form of motion gives life to nuclear one. Steady space thermodynamic potentials are created as the result of nuclear reactions in stars.

That is the possible circulation of forms of motion and energy leading to the restoration of matter thermodynamic activity. But we shall return to terrestrial micro-black holes, which emit various sorts of radiation, in particular, neutrino.

 

6.2. Neutrino radiation of small black holes (to the top). One of small mass oton features is the Hawking effect. The spectrum of black hole (BH) radiation was first calculated by Page [Pa01,2], which then was elaborated [×å01]. The total power of black hole radiation for various cases can be expressed by the formula:

 

P_BH = (k_g + k _n + k _g + k_e + k_N) P_c (M_c/M_BH)²

 

k_g + k _n + k _g + k_e + k_N = 1                                                             (6.2.1.)

 

where the factors (k) mean parts of black hole radiation power, corresponding to different types of particles: k_g (gravitons), k _n (neutrino), k_g (photons), k_e (leptons), k_N (barions).

For any masses (M_âí < 10^10,5 kgs) and large powers of black hole radiation the outputs of radiation essentially depend on the model of strong interaction at superhigh energies and on the spectrum of masses of elementary particles, but this was  investigated insufficiently. Therefore for the spectrum of black hole radiation there are data only for three cases [Ôð01,1], [Íî14], which are given in table 6.2.1.

 

 

Table 6.2.1.

Power and spectrum of radiation of black holes of various masses: P_BH = (k_g + k _n + k _g + k_e + k_N) P_c (M_c/M_BH)²

 

 

 

In connection with principal opportunity of experimental registration of high energy particle radiation, including neutrino, from terrestrial BHs we shall provide more exact accounts of neutrino radiation flow characteristics, according to joint with V.S.Gurin work [Òð41], [Tr42,3,4]. Let us concentrate the attention on the radiation from nonrotating BHs, because integral features of radiation depend a little on the fact of rotation. Besides that, a rapidly rotating, moreover charged, BH inside dense heavenly bodies will quickly lost the moment of rotation and the charge because of interaction with environmental substance.

BH’s mass decrease due to radiation of one kind of particles with quantum numbers l, m, p occurs under the law

 

,                                         (6.2.2.)

 

where Ì is the mass of BH in the moment given, w is the energy of particles (geometrized units G = c = 1 are used ). Taking into account the dominant contribution from modes with I = s = 1/2 for massless neutrino

 

,                                             (6.2.3.)

 

and for massive particles with mass of rest m and spin 1/2

 

.                 (6.2.4).

 

The spectrum of radiation dN/dtd w is determined by the subintegral expression (6.2.2) with the appropriate substitution (6.2.3) or (6.2.4):

 

                  dN/dtd w = G _{w lmp} /(exp(8 p M w ) + 1)                            (6.2.5.)

 

The results of calculations for parameters of BHs, which presumably could be in the Earth’s interiors are presented below.

The spectrum of massless neutrino radiation for Schwartzschild BH is almost the symmetric bell-like curve, the position of which maximum is defined by the mass of BH. One can see the energy of radiated particles to depend essentially on this one BH parameter: so, if the main share of neutrino, radiated by a hole with Ì > 10¹² g, is in the energy range less than 10 MeV, the main contribution from neutrino with energies more than 1 GeV will be in the case of BH with Ì < 10¹² g, and for BH with Ì < 10¹⁰ g neutrino with energies more than 1 TeV are radiated. This is of importance for analysing the problem of registration of neutrino, which appear at the quantum evaporation of micro-BH, since in difference from BH of solar masses, when energy does not exceed 15 MeV, in the case of BH of specified range of masses considerably (in 3-4 orders) more energetic particles should be expected, which can be easier registered because of a greater section of absorption in substance (see below).

The position of maximum in the spectrum defines a rang of neutrino energies, which should be expected from corresponding BH, and it can be determined from the transcendental equation ln (x - 2) = -õ, where x = 8 p M w _max , that gives (in geometrized units):

 

.

 

The complete flow of energy radiated due to process considered as neutrino (or flow of particles) in the whole spectrum or in some spectral interval is obtained by the integration of expressions for dN/d w dt , and it grows strongly with decrease of BH mass.

If one admits the existence of neutrino mass of rest, which is quite probable according the modern data: m( n _e ) < 17 eV; m( n _m ) < 0,27 MeV; m( n _t ) < 35 MeV, it is interesting to analyse features of radiation of these particles due to the Hawking effect, i.e., of particles with the same quantum numbers, but having unzero mass of rest in the formula (6.2.3.).

For neutrino of the fourth generation, for which the estimation of mass is considerably more: m( n ₄ ) ~ 45 GeV, the spectrum of radiation can essentially change, but then the emission of n ₄ will run together with other heavy particles of spin 1/2: protons, neutrons, muons, etc. All the considerably smaller masses for n e  and n m in a case of M_BH less than 10¹⁴-10¹⁵ g do not practically change the spectrum and the total flow of radiated neutrino. In general, the spectrum feature is similar to that for massless particles, and values for complete flow and position of the maximum of spectrum dN/d w dt differ unessentially. The shape of spectra dM = d w dt is similar to that for the number of particles, and its integration gives the rate of BH mass loss, dM/dt, which is turned out to be inverse proportional to ̲.

For deciding question on the registration of neutrino flow from BH, presumably located inside planets, we shall consider estimations for sections of neutrino absorption, for example, n _e , due to interactions with electrons in the nondegenerated electron gas (interactions with nuclons have smaller sections), which can take place at its detecting. The value of the section in strong degrees depends on energetics and it is defined according to the following formulas [La10]:

 

, ,               (6.2.6.)

 

, ,                (6.2.7.)

 

where m is the mass of electron.

It can be noted that in both cases the detecting of particles with higher energy, which share is great for BH of a smaller mass, is more probable. Unlike the case of solar neutrino terrestrial BH can radiate neutrino with energies more than 10³ MeV, which raises the section of absorption in 2-3 orders. Hence, placing the detector of neutrino at the close distance from the presumable BH localization place (its exit on the surface), detectors of already existing designs should detect the sharp excess of the flow of particles in comparison with background and solar ones, and the directivity of this high flow will indicate the possible localization of its source, i.e., BH.

One of such presumable places on the Earth is acting volcanoes [Tr01,5]. However neutrino detectors existing are located regardless to geological activity, therefore abnormal high flows from localized sources could not be detected, since they rapidly decrease when removing from a source.

The formulas above reflect the contribution to radiation from one sort of particles with spin 1/2, but actually BH will radiate other particles too [Pa01,2], [Ol00], [Ma00,1]. To calculate the radiation of three generation neutrino and antineutrino in the case of their masslessness calculated values of a flow should be multiplied by 6. If neutrinoes have unzero mass of rest, the contribution of each type will differ a little, and in view of the problem of registration each type of neutrino must be considered separately.

Since the fourth possible type of neutrino, if it exists, has much more greater mass of rest than others ( ³ 45 GeV), its contribution to BH radiation will will reveal itself already after nuclons and hyperons for BH with Ì << 10¹⁰ g. Black holes should radiate practically all particles down to Plankian ones, that is itself of great scientific importance.

 

6.3. Explosions of micro-black holes. Plankian particles. Theories of the Great Unification (to the top). Explosions of black holes, most likely, occur in the central region of the Earth, which is a kind of a storehouse of pre-explosive and explosive black holes. The spatial region of the terrestrial nucleus is chosen for gravitational objects. This is the region of the most ancient part of the gravitational potential "hole", in which there should be located the most ancient and short-living black holes. This have given a ground for the project of registration of Plankian particles, which are the test for verifying theories of the Great Unification.

In an approach, developed in the monograph, SBH are considered as "germs" (centres of usual substance condensation) of space bodies, which means that SBH are not seized by space bodies, but are originally in them. Three conclusions of especial importance follow from this approach. First, restrictions on number of SBH, connected with the Hawking radiation, are automatically removed (the Hawking radiation is thermolized in a substance). Secondly, the newest cosmological scenario, in particular, the inflationary cosmology opens new opportunities in solving the problem of SBH formation. Thirdly, SBH in composition of planetesimals and asteroids can be seized by a gravitational field of the Earth.

Previous researches on the registration of black hole explosions carried out in the other direction. First, black holes were looked for not in depths of the Earth, but in depths of Space. Secondly, they were tried to detect not by neutrino radiation, but by electromagnetic one. For detecting neutrino bursts it is possible to use any available neutrino detectors, because all of them are almost equally distanced from the region of black hole location. It is desirable only to lower in one order the value of neutrino energy registered. In available deep-water neutrino detectors this value is equal to 50-100 GeV, and to detect a black hole surely for few years before its explosion it is necessary to register neutrino with the energy of the order of 10 GeV.

The pre-explosive black hole with M_BH » 10⁹ kg radiates during few years neutrino with the energy of the order of 10 GeV, the flow of which at the surface of the Earth is j _Å   » 10⁹ m^-2s^-1. The energy and the neutrino flow will grow with time. Last days before the explosion the black hole will radiate neutrino with energy 100 GeV and j _Å   » 10¹⁰m^-2s^-1. The energy and the neutrino flow will begin to grow sharply and last minutes the black hole will radiate neutrino with energy up to 10 TeV, and the flow will be j _Å   » 10¹²m^-2s^-1. The explosion of the black hole is finished by that that in shares of a second the burst of neutrino with the energy more than 100 TeV [Òð11], [Tr05] happens.

Even if there are many pre-explosive black holes, they must explode alone. This is because that with time the difference in masses of black holes influences more strongly upon the processes of their evaporation. For black hole exploding simultaneously, their masses must be equal with high degree of accuracy: so, for black holes with masses of the order of 10¹¹ kg the distinction in the value of masses should not be more than one three-millionth. Thus, black holes come to their finish (explosion) alone and the neutrino radiation from them should start to stand out sharply from the neutrino background formed by pre-explosive black holes.

The research project must develop a practically feasible experiment on registration of terrestrial MBH explosions. First, it concerns the neutrino experiment, since preliminary theoretical developments concerning neutrino radiation bursts from MBH explosions already exist. Secondly, it is possible to put a question on the registration of massive particles (leptons and adrons). This is because that in MBH exploding even at the centre of the Earth it is necessary to expect the increased flow of particles with superhigh energy, since the length of run of ultrarelativistic particles being born turns out to be comparable with the size of the terrestrial radius. The third, the superhard gravitational radiation from exploding MBH requires the analysis of opportunity of its registration. At last, in the MBH exploding there should be seismic waves.

The first task of the project is the determination of neutrino flow through the terrestrial surface and the number of absorption acts near the terrestrial surface from MBH exploding in the centre of the Earth. Then it is necessary to compare these features with the parameters of the available equipment in the registration of superhigh energy neutrino in Dumand and Baykal projects, and with those of other equipment in the registration of superhigh energy particles too. The problem of registration of neutrino flow with quickly varying spectrum requires the analysis: for fractions of a second the value of neutrino energy, from exploding MBH can vary through order. The careful analysis of already available experimental data on registrations of superhigh energy particles will be required both for the reason of revealing neutrino bursts being looked for, and determining possible restrictions on the MBH explosion frequency.

A possibility of massive particle (leptons and adrons) registration is of especial interest, since they are born in enormous number in MBH exploding. This is because the length of run of ultrarelativistic particles being born in the explosion becomes comparable with the radius of the Earth, i.e., the possibility of their registration near the terrestrial surface is opened. Moreover, the registration of neutrino radiation from MBH and the determination of neutrino energy can give the value of the MBH mass. It means, that the time of MBH explosion, i.e., the time of arrival of ultrarelativistic particles at the surface of the Earth, which have superhigh energies down to Plankian values, can be predicted. The previous increase of neutrino energy can be a "sign" of the MBH explosion to come.

Thus, the registration of MBH explosions can open the way of solving the not less important task, i.e., the experimental verification of the united physical theory of all fundamental interactions. Possibilities of technical perfection of colliders for reaching sub-Plankian energies are limited, and the question on natural sources of sub-Plankian energy particles gets up inevitably. Nowadays small black holes are while single objects known in science, which can produce sub-Plankian energy particles. Terrestrial MBH can serve as important elements of a sort of "laboratory" for verifying theories of the Grand Unification or supergravity.

Small as the probability of MBH explosions in the Earth is, the problem of their registration deserves the most careful research, since it is only the way to know anything about maximum large energy physics from the experiment. Moreover, there are geophysical certificates of black hole evaporation and explosions, some of which will be pointed out in short in the following section.

 

6.4. Relativistic geological petroleum exploring and thermonuclear reactions in the terrestrial interiors (to the top). The existence of otons in the Earth must lead to geological consequences. This is because terrestrial surface regions, close to which black holes are located, should be peculiar in the geological attitude, since oton influences can be accumulated for a long time [Òð11].

Any deposits of useful natural resources mean the certain degree of localization, which can be probably explained by some oton influences. In geology the correlation of the ancient volcanism with any deposits of useful natural resources was noted long ago. Since the volcanism can be connected with the action of otons, and the localization of otonic singularities in the Earth is ordered in certain way, it is possible to predict the localization of deposits at the surface of the Earth.

The Earth, in some sense, is the chemical anomaly, since its structure extremely differs from the average chemical structure of space substance, in which hydrogen and helium dominate. This is explained by that that easy gases (hydrogen and helium) during the evolution have been evaporated from the substance of the Earth. Howerver abnormal amounts of an easy isotope of helium-3 detected in the terrestrial interiors collides with the hypothesis about the evaporation of helium, since helium-3 can be formed only in result of thermonuclear reactions.

To avoid this contradiction it is necessary to assume the terrestrial origin of helium-3 as a result of thermonuclear reactions. It will help to eliminate difficulties connected with the formation of some heavy elements [Òð16]. Therefore, it is not excluded, that in magmatic chambers of volcanoes the element formation occurs, on which the correlation of ³Íå anomalies with volcanoes shows.

The decay of fermi-otons can lead to the formation of transuranium element deposits. The evaporation and explosions of black holes can reveal the mystery of kimberlite pipes, with which the deposits of diamonds are connected [Òð16].

Otons with appropriate parameters can be sources of energy for the formation of chemical compounds, gaseous and liquid energy carriers (hydrocarbons). Revealing the spatial arrangement of otons in the Earth, relativistic (otonic) geology can predict the localization of huge deposits of petroleum and gas in non-traditional geological regions [Òð15]. In any theory of the hydrocarbon origin (organic or inorganic) the source of energy for their formation is required. Such sources can be otons.

The appearance of otons in the deposit of hydrocarbons should be accompanied by variations of gravitational and electromagnetic fields, that brings essentially new elements in geophysical exploration. Otons can be detected by these especial variations of physical fields. Moreover, the detection of huge deposits of petroleum and gas near converting complexes or megapolicies becomes possible [Òð15]. This will give not only the vast incomes due to the sharp reduction of transport expenses, but also will lead to the reduction of ecological catastrophe danger.

Black hole evaporations and explosions transform matter from its superdense state in usual one, that leads to the grandiose expansion of volume occupied by substance. Since in MBH evaporating (or their colliding) the significant part of energy is carried away in space in the form of radiation — (gravitational, neutrino and others), which weakly interacts with terrestrial substance, it can result in the reduction of the total mass of the Earth. All these properties of terrestrial otons can be involved to explain the mechanism of expansion of the Earth, the idea of which is introduced in one of the theories of geodynamics [Êý00].

According to this geodynamic idea for 200 millions years the Earth should expand on 20 % from its initial volume. Such the expansion can provide the transition of substance from the otonic, superdense state in usual one, which runs with the rate 10⁸ kgs/sec. For providing the such speed of substance receipt from otons, hundred millions evaporating black holes with Ì_î = 10⁹ kgs must be in the Earth simultaneously [Tr05]. Certainly, the mass spectrum of black holes providing the arrival of usual substance in the Earth from otons can be the most different, as well as black hole manifestations near the terrestrial surface can be so different.