{'fraction_non_alphanumeric': 0.025440123815051268, 'fraction_numerical': 0.009092667827432772, 'mean_word_length': 4.715312327252626, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 1, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A Challenge to Control Gravity via Applying Electromagnetic Low-Frequency Radiation - Theory and Proposed Model Experiments

Including Vaidya metric into the model of Expansive Nondecelerative Universe allows to localize the energy of gravitational field. A term of effective gravitational range is introduced and classic Newton potential is substituted for Yukawa-type potential. It allows to allocate a typical frequency value to each gravitational field. Derived theoretical conclusions led us to investigate the effect of electromagnetic field with a precisely predetermined frequency and intensity on iron. We believe that under certain circumstances a decrease in iron gravitational mass should be observed. Two model experiments verifying the theoretical conclusions are proposed.


Introduction
Among the main parameters describing the fundamental physical field, its static potential ϕ should be introduced. This potential contains a dumping function e δ r , in which δ means a reciprocal value of the Compton wavelength of the corresponding boson mediating a given interaction. The dumping function plays a fundamental role for the short-range fields. For both the gravitational and electromagnetic interactions the value of the function is close to 1. Having, however, a medium with a higher amount of charged particles, the dumping function for electromagnetic interaction adopts the form e -r/d , where d is so-called Debye length. It means that the potential of a given particle is shielded by its neighbouring charged particles and in a distance r above d it approaches zero value. All these facts are well-known.
In this contribution a new dumping function, namely e − r / r ef , is introduced for gravitational field, where r ef expresses the effective gravitational range of a body. Its meaning lies in the presumption that in the distance r exceeding the effective range, the gravitational potential of a body is shielded by the neighbouring mass and drops down to non-measurable values. Provided that the mean Universe mass density is known (and it is known relatively precisely), this effective range may be determined b) The curvature index k and Einstein cosmologic constant Λ are of zero value c) The mean energy density of the Universe is identical just to its critical density. d) Since a is increasing in time, m u must increase as well, i.e. in the ENU, the creation of matter occurs. The total mass-energy of the Universe must, however, be exactly zero. It is achieved by a simultaneous gravitational field creation, the energy of which is negative. The fundamental mass-energy conservation law is thus observed.
e) Due to the matter creation, Schwarzschild metrics must be replaced in ENU by Vaidya metrics [10 -12] in which the line element is formulated as r r and the scalar curvature R (which is, contrary to a more frequently used Schwarzschild metric of non-zero value in Vaidya approach also outside the body allowing thus to localize the gravitational energy density) in the form where m is the mass of a body, G ( 6.67259 10 − 11 kg − 1 m 3 s − 2 ) is the gravitational constant, r is the distance from the body, r g is the gravitational radius of the body, f (m) is an arbitrary function, and Ψ is defined [7] as In order to f (m) be of nonzero value, it must hold Dynamic character of the ENU is described by Friedmann equations.
Introducing dimensionless conform time, equation (1) can be expressed as from which a  da (10) dη Applying Vaidya metric and stemming from Robertson-Walker approach, Friedmann equations [13] can be then written in the form where ε is the critical energy density (identical to the actual density within the ENU model) and p is the pressure. Based on (11) and (12) it follows for energy density of the Universe within the ENU Equations (13) and (14) represent the matter creation and the negative value of gravitational energy, respectively (for more details, see [3 -5]).
A typical feature of the ENU model lies in its simplicity, in the fact that no "additional parameters" or strange "dark energy" are needed, and in the usage of only one state equation in the Universe description. Calculated gauge factor a, cosmological time t u , and energy density ε match well the generally accepted values.
Owing to Vaidya metric application, the ENU model enables to localize gravitational energy [7]. Stemming from a general formula [7], the absolute value of gravitational energy density ε g is a function of a body mass m and the distance r from the body R c 4 3 mc 2 The absolute value of the gravitational field density of a system equals to the critical density at the distance r ef (effective interaction range of its gravitational force).
Comparison of the relations (13) and (15) Gravitational Yukawa potential and its consequences for micro-world and cosmos In a certain approximation, the effective range r ef may be understood as Compton wavelength of the interchanged particle mediating a corresponding physical interaction (in such a case, r ef represents the graviton wavelength and c/r ef its frequency).The heavier the body, the longer length of its effect (the longer its effective range) and, in turn, the lower frequency must have the related quantum of gravitational field.
From the viewpoint of theory, there is not limit in the range of gravity, however, in a distance r exceeding the given effective range r ef , the body gravitational effect strongly drops and becomes immeasurable.
The Universe effective range as a whole equals to its gauge factor a (about 1. At the end of this part, one interesting fact is worth mentioning. The effective range of the neutron is currently close to 1.8 x 10 -14 m. To initiate a creation of a neutron star, the neutrons must be packed closer, i.e. the mass density must be higher than 6.9 x 10 10 g/cm 3 . And it is just the case. It has been calculated and rationalized very precisely that for starting a creation of a neutron star, the density must be at least 4.3 x 10 11 g/cm 3 . This density is associated with the effective range of the neutrons at about 4 billion years following the beginning of the Universe. The first neutron star of our Universe might be created approximately 10 billion years ago.

4.
Case studyexperiment 1 The case study deals with the effect of low-frequency electromagnetic field on iron materials.
The characteristics of electromagnetic field, in particular its frequency f, power P and intensity I are dependent on the iron conductivity σ, permeability , mass m and thickness. It holds for the metal skin layer δ: The following condition (22) is required to be met where r ef is the gravitational range of the metal sample (see eq. 16 ), and δ is its thickness.
Frequency of electromagnetic radiation to be used must comply with relation (23) in order the whole mass of the metal sample m tot be eliminated at the condition (22).
Such parameters are, however, reached and maintained only with difficulty. This is why the condition (22) may be moderated as follows where m x is part of the sample to be compensate using electromagnetic radiation with the frequency corresponding to the skin layer δ.
Integration of (15) over volume and subsequent derivation of the integration product according to time lead to relation specifying the gravitational power. Electromagnetic power must be identical. It must therefore hold If S is the body surface affected by electromagnetic radiation, the radiation intensity is Provided that our sample will be exposed to electromagnetic radiation with the corresponding frequency and intensity, the body mass should be reduced by m x .
An alternative approach lies in the possibility to encapsulate the electromagnetic radiation antenna directly into a body with the wall thickness 2δ. Frequency, power and intensity of electromagnetic radiation are obtained by similar procedure.

5.
Case study -experiment 2 Let us have an iron cubic sample (r = δ = 5 x 10 -2 m) with the following parameters: With the samples made from identical material, the intensity of electromagnetic radiation does not depend on the sample dimension. The greater the cube, the higher its mass reduction in absolute value (and lower its efficiency), the higher must be electromagnetic power but lower its frequency The frequency can be reduced if a material with a higher permeability is used. It would be very stimulating to experimentally find whether increasing the electromagnetic radiation intensity will cause an increase m x , i.e. the process efficiency.

Conclusion
It should be pointed out that in the issue of mass reduction, the main role is played by the intensity and power of electromagnetic radiation. Within the same time, the gravitational and electromagnetic energies passed through the body must be identical.
Due to the different rate of electromagnetic energy transfer through the body, the electromagnetic and gravitational frequencies are not and cannot be, however identical.
The precisely predefined electromagnetic frequency ensures only the total absorption of the electromagnetic radiation in the body and the interference of both fields. This interference should result in the body mass reduction. It is worth mentioning that there is no violation of the energy conservation law, since immediately after the termination of electromagnetic field action, the original mass is returned.
Owing to its precisely defined and known parameters, iron is ideal testing material.
It is not, however, the only way to change the mass of materials. Within the experiment the electromagnetic radiation intensity was about 2 x 10 9 J/m 2 s, which is a value close to the gravitational field intensity of the Earth. We believe that the interference of the both field caused gravitational pulses having the same translation direction as the original electromagnetic pulse. Podkletnov succeded in measuring not very substantial but verifiable reduction in the mass of bodies exposed to the pulse.
It might be a case that an analogous mechanism applies in the solar corona heating.
The We would like to put stress on the necessity of performing further experiments accompanying the theoretical research. It is obvious that for building-up the quantum theory of gravity, a wider and more complex basis must be formed than the general theory of relativity. 7.