5. Gravimetric registration of terrestrial black holes

 

5.1. Short-term variations of gravitational potential derivatives produced by moving otons.
5.2. Determination of oton mass by physical quantities registered.
5.3. Registration of the gravitational potential second derivative minute variations with a variometer.
5.4. Discovering of gravitational force short-term variations with the gravimeter.
5.5. Project to synchronous registration of short-term variations of the gravitational potential first and second derivatives.
5.6. Cities as technogeneous indicators of terrestrial black holes.
5.7. Empirical evidences of short-term local inversions of the gravitational force.

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5.1. Short-term variations of gravitational potential derivatives produced by moving otons (to the top). Terrestrial otons can be registered immidiatly by their gravitational field: they produce short-term local gravitational anomalies [Òð06‑11], [Tr04‑08].

Otons are till noticed to be in principle such objects of physics to have been predicted and discovered on the Earth as, for example, intermediate vector bosons (W⁺, W^-, Z⁰). Intermediate vector bosons were discovered in famous experiments of C.Rubbia, which complicated and very expensive equipment was specially prepared for. But in the case of oton's registration the situation is quite analogous to which was in discovering of relic radiation, when the available equipment has been used. The modern gravimetric equipment [Ãð00], [Ãð20,1] registers the first vertical derivatives of the gravitational potential (g, gravimeters) and its second horizontal derivatives (W_xx, variometers). Let us analyse the behaviour of the first and the second derivatives of gravitational potential produced by otons.

Analysing temporal varations of the first ( D g) and the second ( D W_xx, D W_zz) gravitational potential derivatives forced by moving near the Earth's surface otons we shall take into account only two components of the oton motion. The first, it is a free oton fall in the Earth's gravitational field (the motion along the Z-axis). Degenerated (oscillatory) orbits are considered. The second, it is the oton motion relative to the Earth surface (the motion to the West along the X-axis), arising by due to the rotation of the Earth. Tsese simplifications are quite justified for otons which orbit apocentres are close to the Earth surface.

Under such simplifications the time dependence of gravitational potential derivation variations caused by otons will determined by expressions:

 

ааааааааааааааааааааааааа ,ааааааааааааааааааааааааааааааааааааа (5.1.1.)

 

ааааааааааааааааааааааааа , аааааааааааааааа ааааааааааааа(5.1.2.)

 

ааааааааааааааааааааааааа ,аааа аааааа а ааааааааааааааааа (5.1.3.)аааааааааааааа

 

аааааааааааааааааааа ,аааааааааа ааааааа а аааааааа (5.1.4.)

 

X₀, Ó₀ are coordinates of oton orbit apocentre, Ì_î is an oton mass, V _j - linear velocity the earthly surface point movement at breadth of j (at breadth of Obninsk V _j == 267 m s^-1). Gravitational potential derivatives are conneced with each other by the expressions:

 

аааааааааааааааааааа , ааааааааааааааааааааа а(5.1.5.)

 

ааааааааааааааааааааа , аааааааааааааааааааааааааааааааааааааааааааааааааааааааа а(5.1.6.)а

 

ааааааааааааааааааааа , аааааааааааааа а(5.1.7.)

 

а

 

 

 

 

 

Fig. 5.1.1. In the figure the Z-axis is directed vertically, the X-axis is directed along the breadth and it is tangent to a point of the observer (X = 0, Z = 0) being at the surface of the Earth. Different parabolas mean different otonic trajectories inside or near the radius of registration (R_r = 100 km). The specifity of gravitational potentioal variations is followed from allocation features of otonic orbits with respect to the observer. To a various position of parabolas there correspond various combinations of gravitational potential derivatives, both positive, and negative.

 

 

Coordinates of an oton orbit apocentre influence not only quantitatively, but also qualitatively on the otonic graviimpulse picture. Trajectories of otonТs orbits are shown in Fig. 5.1.1., which are in limits (or near) of registration radius with respect to the coordinate system of the observer who is residing on the earthly surface. Already from the character of these orbits, or more precisely, from features of their arrangement with respect to the observer it is obvious, insofar different can be the character of the otonic graviimpulse. The short-term increase of gravitational force, which is then exchanged by its decrease, is the most simple case. But there can be more complicated variants, when in short time different and even opposite gravitational potential derivatives variations are possible, for example: (+g, +W_zz), (-W_xx), (-g, -W_zz), (+W_xx).

To express the dependence of gravitational potential derivatives upon the time more explicitely, we consider a more simple case (X₀ = 0; Z_o = 0). This condition results in simplification of expressions (5.1.1.) Ч (5.1.7.) and gives:

 

, ааааааааааааааааааааааааааааааааа а(5.1.8.)

 

ааа , ааааааааааааааааааааааааааааааааааа а(5.1.9.)

 

D W _xx = 2V _j GM _o (V _j ² _а + g²t²/4 )^-2t^-3ааааааааааааа ааааааааааааааааа а(5.1.10.)

 

, аааааааааааааааааааааааааааааааааааааааааааа а аааааааа аа(5.1.11.)

 

, ааааааааааааааааааааааааааааааааааааааааааааааааааааааааааа ааа(5.1.12.)

 

.аааааааааааааа аааааааааааааааааааааааа аааааааааааааа(5.1.13.)

 

The time dependence is different in two cases:

1) t < 2V _j /g, 2) t > 2V _j /g. The first condition for (5.1.8.) Ч (5.1.10.) gives the following expressions:

 

аааааааааааааааааааааааааааааааааа , ааааааааааааааааааааааааааа а(5.1.14.)

 

аааааааааааааааааааааааааааааааааа , аа а ааааааааааааааааа а(5.1.15.)

 

аааааааааааааааааааааааааааааааааа . аа а ааааааааааааааааа а(5.1.16.)

 

аExpressions (5.1.14) Ч (5.1.16) show that the change of gravitational potential derivatives caused by the oton, which is near of apocenter, is defined by the rate of the EarthТs rotation. But through about one minute the vertical component of oton velocity becomes significant due to the free fall acceleration in the gravitational field of the Earth. It corresponds to the second condition, which in a limiting case from (5.1.8)Ч(5.1.10) gives following expressions:

 

, ааааааааааааааааааааааааааа (5.1.17.)

 

, ааааааааааааааааааааааа (5.1.18.)

 

, аааааааааааааааааааа а(5.1.19.)

 

Expressions (5.1.17.) Ч (5.1.19.) mean, that at the given stage the change of the otonic graviimpulse is determined by the otonТs acceleration in the gravitational field of the Earth. Expressions (5.1.14.) Ч (5.1.19.) clearly show that otonТs gravitational manifestations have pulsed character. Gravitational anomalies caused by the oton rapidly reach the maximum and so rapidly (in inverse proportion to time in fourth - seventh degree) decrease.

From said above and expressions (5.1.8.) Ч (5.1.19.) it follows, that for registration of otonic graviimpulses it is necessary to remove gravimetric data every second and there should not be an averaging on large time intervals. As a result of such the "averaging" the otonic graviimpulse seems to be УerasedФ and the oton manifestation is not fixed by the device. Then, the amplitude of graviimpulses should be on the order above than the accuracy of the device, in order to be possible to resolve temporary structure of the otonic graviimpulse.

Otonic graviimpulses have rather specific structure: the time of about one minute; amplitudes corresponding to gravitational masses in millions and billions of tons; temporary variations of otonic graviimpulse corresponding to extremely fast motions of supermassive bodies.

Besides it is possible to specify additional, characteristic only for otonic graviimpulses, features (see Fig. 5.1.1.): 1) negative variations of the gravitational potential vertical derivative (- D g, - D Wzz), which means that cases of the gravitational force inversion must occur; 2) short-term variations of the gravitational potential horizontal derivative (+ D Wxx, - D Wxx); 3) the quick change (within few minutes) of different kinds of gravitational potential derivatives variations (+ D g, + D Wzz, - D Wxx, - D g, - D Wzz, + D Wxx, + D g, + D Wzz,); 4) arisings of magnetic and other geophysical fields micropulsations, synchronous with graviimpulses.

Thus, to registrate otons is desirable to realize complex geophysical experiment, in which the registration of geophysical fields should be carried out with high temporary resolution not only by gravimeters, but also by variometers, magnitometers and other geophysical equipment. In any experiment on registration of otons it is necessary to estimate the order of their masses value, to which the following item is devoted.

5.2. Determination of oton mass by physical quantities registered (to the top). There are several independent ways to determine the oton mass through observable physical quantities, namely, through direct gravimetric measurements of gravitational potential derivatives variations, produced by otons.

If variations of the gravitational potential vertical derivative are mainly registered ( D Wxx << D Wzz), then using expressions (5.1.1.) Ч (5.1.4.) it is possible to obtain the value Ìî through observable values of the gravitational potential derivatives magnitude and through the time of their registration (tk):

 

ааааааааааа , ааааааааааааааааааааааааа а аааааааа а(5.2.1.)

 

аааааааааа , ааааааааааааааааааааааааааааааааа а(5.2.2.)

 

The maximal values of the gravitational potential first and second derivatives magnitude are equal accordingly to: D g (0), D Wzz (0). Registrating horizontal otonic graviimpulses ( D Wxx >> D Wzz), by use of (5.1.5.) Ч (5.1.6.), the oton mass can be determined through the expression:

 

ааааааааааааааааааааа ^,ааааааааааааааааааааааа (5.2.3.)

 

D W_xx (0) Ч maximal value of gravitational potential horizontal derivative. It is possible to determine the oton mass through expressions which do not contain time explicitely. For this simultaneous measurements of various gravitational potential derivatives are necessary, and from (5.1.1.) Ч (5.1.4.) we have for oton mass:

аааааааааааааа , ааааааааааааааааааааааааа а(5.2.4.)

 

Atа D W_xx << D W_zz

 

аааааааааааааааааааааа , аааааааааааааааааааааааааааааааааааааааааа а(5.2.5.)

 

Because of modern variometers do not register directly the value of the gravitational force vertical gradient (W_xx), for its determination it is necessary to use two synchronously working gravimeters, carried on height h = D Z. In this case D W_zz = [ D g(2) - D g(1)] h^-1. But having two series of synchronously determined values of the otonic graviimpulse first gravitational potential vertical derivative [ D g(1), D g(2)] it is possible to determine the oton mass directly through them:

 

ааааааааааааааааааааааааа , ааааааааааааа а(5.2.6.)

 

Registrating simultaneously the gravitational potential second horizontal derivative [ D W_xx (1), D W_xx (2)] by variometers, being at the distance l from each other, the value of the oton mass will be determined through the expression:

 

аааааааааааааа , аааааааааааааа а(5.2.7.)

 

Knowing the parameters of gravitational potential derivativeТs variations it is possible to determine through expressions (5.2.1) Ц (5.2.7) the mass of the oton, which has caused this variation, i.e., it is possible not only to fix the very fact of the black hole gravimetric registration, but to determine the order of its mass value.

5.3. Registration of the gravitational potential second derivative minute variations with a variometer (to the top). Gravitational potential derivatives minute variations predicted within the framework of the intraterrestrial black holes concept [Òð11], [Tr04] were found out by the author in the experiments have been carried out [Òð13,4], [Tr06,7]. As it was already noted, the registration of gravitational potential derivatives minute variations Ч otonic graviimpulses Ч ÎGI (see 5.1.) means the discovering of intraterrestrial black holes.

The experiment on registration of the gravitational potential second derivative short-term variations have been carried out by the author with the variometre Å-60 in the Obninsk geophysical observatory (the Institute of physics of the Earth, the Academy of Sciences of the USSR) in June, 1991. Before proceeding to the discussion of experimental results, let us note that the question on gravitational potential derivatives short-term (minute) variations neither in the theoretical aspect, nor with respect of their experimental registration was not put earlier in gravimetry [Ãð00], [Ãð20,1], [Ïî00,1]. Therefore it was necessary to carry out a preliminary experiment on revealing the reaction of Å-60 on short-term gravitational influences.

The sensitivity of variometer Å-60 allows to register at close distances the gravitational mass of the operator: Ì₀ (kg) = 7,5 (R₀m)³. A gravitational mass of 60 kgs is registered at distances up to 2 m, 80 kgs Ч2,2 m, 117 kgs Ч2,5 m, 200 kgs Ч 3 m, 1 ton Ч 5 m. Thus, the operator, coming to the variometer at distances less than 2 Ц 2,5 m, causes such changes of the gravitational potential second derivative, which are registered by the variometer. This circumstance has allowed the author to carry out the experiment on revealing of variometre Å-60 reactions on short-term gravitational influences, which results are provided in Table 5.3.1. The experiment was carried out from 14h 30m (08. 06.1991) to 5h 30m (09. 06. 1991) of the world time.

Two available registerring systems of the variometer (two beams) can react differently depending on the master mass location: 1) indications of both systems can simultaneously increase or decrease; 2) indications of registerring systems vary in opposite phase (for one system indications increase, and for another one they decrease and vice versa); 3) the gravitational mass can be registered by only one of the systems, but the other one has practically no response. The time of gravitational influence recording appears several more times than the time of the gravitational influence itself (Table 5.3.1.). Gravitational influences with a duration of the order of a second are not already detectable by the device.

 

аTable 5.3.1.

Duration (in min) of the master gravitational mass influence, ( D t_GI ), and duration of registration of a gravitational impulse from the master mass (Ì_mа85 kgs) by the Å-60 variometre, ( D t_E-60 ).

 

 

 

Severeal minute variations of the gravitational potential second derivative were detected from 5h30m UT (09.06.1991) to 5h30m UT (10.06.1991) in the Obninsk geophysical observatory with the Å-60 variometer, of which three possess enough explicit structure for their identification with ÎGI: 1) t₀ = 08^h14^m (09.06.1991), D t_E-60а = 9 min, D t_OGI = 2 min; 2) t₀ = 15^h19^m (09.06.1991), D t_E ‑60 = 7.4 min, D t_OGI = 1 min; 3) t₀ = 05^h00^m (10.06.1991), D t_E-60 = 12.6 min, D t_OGI = 6 min. As it is obvious from aforsaid, the duration of the gravitational potential second derivative variations registered coincides in a suprising way with those predicted by the ÎGI theory [Òð11], [Tr04] (see also Table 5.3.2). The identification with ÎGI is also supported by the fact that no gravitational impulses with duration about an hour or more were discovered, i.e., with a duration which would clearly contradict the ÎGI theory.

 

 

 

 

Table 5.3.2.

Duration (in s) of variations of the gravitational potential second derivative tOGI for which the amplitude of otonic gravi-impulse (OGI) decreases in k time for different values of oton orbit apocentre coordinates . аis approximately equal to аfor corresponding values of k.

 

   

Different estimations of otonТs masses (see item 5.2. and Tables 5.3.1. Ц 5.3.2.) give valuesа of the order 10¹⁷ g and more, i.e., the objects which caused minute variations of the gravitational potential second derivative registered in the experiment are, all of them, otons.

5.4. Discovering of gravitational force short-term variations with the gravimeter (to the top).

For the justification of OGI registration the realization of experiments on detection of short-term variations of the gravitational potential first derivative (GPFD) would be purposeful. October 29, 1991 the author performed the experiment on registration of GPFD variations in Institute of Geology and Fuel Minerals Exploitation (IGFME, Moscow ).

Two independent gravimeters by the type of Scintrex CG-3 (Autograv - Automatic Gravity Meter) were used in the experiment. These two independent gravimeters were located in the same cellar room. Values of GPFD were registered every minute. Three synchronous GPFD variations were detected by two gravimeters, and they have rather significant amplitudes and a number of GPFD with small amplitudes (Fig. 5.4.1).

It is hard to explain these GPFD variations by apparatus errors, since gravitational impulses were registered synchronously by two independent gravimeters. Because of these devices location in the same room it is possible to try to explain these sharp synchronous variations of gravimeterТs indications by local technogeneous sauses of the mechanical, electrical, etc. nature. To eliminate such local influences upon experimental results, it is necessary to separate gravimeters enough far apart.

 

 

 

 

 

Fig. 5.4.1.

 

There are also a number of GPFD variations with small amplitudes (of the order of 0,05 mGal) which are correlated with one another (Fig. 5.4.1). These correlations (for example, Уa" and "b"), likely, are not casual, and GPFD variations have the general gravitational nature. The parameters of GPFD variations which were registered by the two gravimeters synchronously correspond to the theory of otonic gravitational impulses.

5.5. Project to synchronous registration of short-term variations of the gravitational potential first and second derivatives (to the top). The long-term investigative purpose is the registration of terrestrial small black holes which have different massess and areas of localization in the Earth. Experiments on registration of gravitational potential derivativeТs variations performed have following lacks: the limitedness of the time of gravimetric data recording, the insufficient degree of temporary resolution, too close arrangement of gravimetric recording systems one to another, the absence of seismic control.

The next experiment is planned to carry out by useing at least three independent recording systems: two systems of the Å-60 variometer and the gravimeter registering tides. The seismic control of the experiment will be provided. The temporary resolution of gravitational signals is expected to be of the order 1 s, the duration of registration Ч 10⁶ s. For increasing the cleanliness of the experiment and controling other geophysical fields is planned making use the magnitometer, the sloppmeter, the sensor of air density, etc.

Let us note that gravitational potential derivativeТs variations in the range of small amplitudes caused by distant otons put a limit on the accuracy of gravimetric measurements and on the determination of the gravitational constant. In other words, the gravitational field of the Earth constantly "trembles", and otonic variations of the gravitational field create the incurable "gravitational noise".

By due to synchronous registration of the gravitational potential first and second derivatives it is possible to increase in this experiment the accuracy of mass spectrum determination in two orders. The even more radical project of terrestrial otonТs registration should use the influence of terrestrial otons on the technosphere, in particular, on cities.

5.6. Cities as technogeneous indicators of terrestrial black holes (to the top). The alternative approach to registration of terrestrial S_BH consists in establishing of a gravimetric equipment in cities, instead of far from them. This is because black holes appearing near to the earthly surface can influence considerably upon the nearest objects, but in the distant deserted areas are there no witnesses of black holes manifestations. The situation is radically different in cities.

The density of population in cities in one thousand times more than the average density of population of the Earth, and it means that only one thousandth of the earthly surface has observers of short-term otonic manifestations. In other words, there are more than one thousand unobservable black holes per an observable one. In a city the black hole can be observed in thousands times more often, than in any region of the earthly surface.

аThis is not yet all. If the tree, pulled out by a black hole, will hardly pay the special attention of the people, the destruction of a multi-storey building (the probability of hit in it is proportional to the cube of the linear size) cannot remain unnoticed in a city. Besides of direct witnesses of such events both inhabitants of a city and of a planet can learn about it through the mass media. If gravimeters and variometers have registered OGI synchronously, the gravitational nature of the building destruction would find the scientific motivation. So, all the technogeneous environment and building of a city can be independent certificates of black holeТs manifestations.

But of the most interesting is that gravitational potential variations are so considerable, that inversions of the gravitational force frequently occur. Short-term local inversions of the gravitational force were already observed repeatedly and there are numerous evidences of similar phenomena, though till now there was no adequate interpretation of these facts.

5.7. Empirical evidences of short-term local inversions of the gravitational force (to the top). It is possible to detect gravitational potential derivativeТs variations by the direct observation of short-term local inversions of the gravitational force, which have the pulsed nature (see item 5.1.). It is a kind of gravitational pushes directed opposite to the Earth attraction. Further we shall note some phenomena, which testify the noticeable value of otonic gravitational impulses.

The tornadoes manifest themselves as antigravitational whirlwinds which working contrary to the force of gravitation lift upwards various things, animals and people [Õå00], [Êà10]. The fall of various objects from the sky (pieces of ice, dead people, stones, metalic things and others) [ÕÕ00] and strange "rains" [Ëà10] consisting of fishes, frogs, grains, coins, etc. tell us that these things were in due course lifted highly in the sky notwithstanding to the force of gravitation of the Earth. The only small part of such phenomena is accessible to observations.

There are numerous manifestations of gravitational force inversions at gravi-tectonic building destructions up to evidences about that buildings rose and hanged momentarily in the air [Áà10]. The brightest phenomenon of such kinds was the event in the town Sasovo of the Ryazan region which has occurred in April 12, 1991 . In the result of the Sasovo event the funnel by a diameter of 28 meters and depth up to 4 meters was formed, and the large part of the ground has disappeared from this place without leaving any traces [×å20]. From words of eyewitnesses, at the Spitak earthquake the whole layers of ground, houses, people, buses rose upwards. At the Zaysan earthquake thousands tons of water have risen from the lake [Áà10].

Similar evidences can be continued, but they have common faults: the low degree of reliability of evidences of people who are in an extreme situation, and the impossibility of similar phenomena reproduction. In this respect experiments on the gravimetric equipment favourably differ. Therefore the complex experiment in the megapolicies could connect advantages of these two approaches.

аTo increase the reliability of otonТs registration there would be useful other properties of terrestrial black holes. In this respect the quantum radiation of micro-black holes is of importance, which will be a subject of the following chapter.