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The information paradox first surfaced in the early 1970s when Stephen Hawking of Cambridge University suggested that black holes are not totally black. Hawking showed that particle-antiparticle pairs generated at the event horizon—the outer periphery of a black hole—would be separated. One particle would fall into the black hole while the other would escape, making the black hole a radiating body. Characteristics of the emission and absorption of usual substance by a black hole can be described by information models. Estimation of the volume of information in black holes is necessary for generation of restrictions for their formation, development and interconversion. Information is an integral part of the Universe. By its physical essence information is heterogeneity of matter and energy. Therefore information is inseparably connected with matter and energy. An information approach along with a physical one allows to obtain new, sometimes more general data in relation to data obtained on the ground of physical rules only. The author’s works, testify about the practicality of information laws usage simultaneously with physical rules for cognition of the Universe. The results presented in this paper show the effectiveness of informational approach for studying the black holes. The article discusses the following questions: The volume of information in the black hole; Information model of a black hole; Characteristics of the emission and absorption of usual substance by a black hole describes the information model of a black hole; The information paradox; A simple explanation of the information paradox by the information model of a black hole.

The information paradox first surfaced in the early 1970s when Stephen Hawking of Cambridge University, building on earlier work by Jacob Bekenstein at the Hebrew University of Jerusalem, suggested that black holes are not totally black. Hawking showed that particle-antiparticle pairs generated at the event horizon―the outer periphery of a black hole―would be separated. One particle would fall into the black hole while the other would escape, making the black hole a radiating body. Hawking’s theory implied that, over time, a black hole would eventually evaporate away, leaving nothing. This presented a problem for quantum mechanics, which dictates that nothing, including information, can ever be lost. If black holes withheld information forever in their singularities, there would be a fundamental flaw with quantum mechanics.

The significance of the information paradox came to a head in 1997 when Hawking, together with Kip Thorne of the California Institute of Technology (Caltech) in the US, placed a bet with John Preskill, also of Caltech. At the time, Hawking and Thorne both believed that information was lost in black holes, while Preskill thought that it was impossible. Later, however, Hawking conceded the bet, saying he believed that information is returned― albeit in a disguised state. At the turn of this century, Maulik Parikh of the University of Utrecht in the Netherlands, together with Frank Wilczek of the Institute of Advanced Study in Princeton, US, showed how information could leak away from a black hole. In their theory, information-carrying particles just within the event horizon could tunnel through the barrier, following the principles of quantum mechanics. But this solution, too, remained debatable [

The basic law of Zeilinger’s quantum mechanics postulates that the elementary physical system (in particular, fundamental particles: quark, electron, photon) bears one bit of information [

constant, c is the speed of light, k_{B} is the Boltzmann constant, G is the gravitational constant, and

The information volume contained in the black hole is proportional to its squared mass. How to explain it? Let us assume that a black hole contains

Let us compare the estimates of squared mass of a black hole:

particle,

Therefore, a black hole is the aggregate of particles (let us call them black particles) each having a mass equal to 0.23th of Planck mass) and interacting with all other black particles that form a black hole. Characteristics and models used in the paper are taken from [

Suppose that at the initial instant of time a black hole consisting of

decreases) by black particles (quanta)

information remaining in the black hole is

For further estimates we implement the law of conservation of uncertainty (information) [

In virtue of energy conservation principle

In the case of a black hole containing one black particle the radiation frequency is maximal and in inverse proportion to Planck time unit. Similar dependences are true for absorption of photons by black holes.

In the general case, there must appear

In the general case, there must appear

In the general case, there must be absorbed

In the general case, there must be absorbed

Identical dependencies are true for cases when photons are absorbed by black holes. In virtue of the law of conservation of uncertainty (information), the changes in the system “a black hole with the mass

Having the estimates of black holes distribution by mass one can calculate the intensity of aggregated distribution of black holes radiation by frequencies and compare them with the experiment results. From the obtained radiation frequency expression one can draw the estimate of black hole radiation temperature. We calculate the temperature of the radiation of a black hole. The thermal radiation of a black body is related to the

average energy of radiation

1) The volume of information in the black hole is proportional to the square of the mass black hole.

2) The information model of a black hole is:

・ A black hole is the aggregate of

・ The black hole is described with the wave function

・ Volume of information in the system described with the present wave function is equal to

3) The temperature of the radiation of a black hole coincides up to a factor

4) A simple explanation of the information paradox with the information model of a black hole and the laws of conservation of uncertainty (information) and of conservation energy was made.

The author thanks N. Kardashev, I. Novikov, I. Sokolov, S. Shorgin, V. Sinitsin, V. Lipunov, L. Gindilis, M. Abubekerov, and especially A. Panov for the shown interest and support of this direction, and also for useful discussions of stated ideas.