ABSTRACT
A process is presented that attempts to explain how black holes could form. According to the usual description, a black hole is the end result of the indefinite collapse of a neutron star under its own gravity until it becomes a point that retains the original mass of the neutron star. In addition to this object, which could be called a "punctual black hole", two other possibilities for the formation of black holes are considered, which we call "material black hole" and "energetic black hole".
A "material black hole" would be the result of a neutron star being compressed beyond the known limit until it becomes a stable body of unknown nature and very high density from which no light can escape.
An "energetic black hole" would be the result of the conversion of all the matter in a neutron star into radiant energy according to Einstein's well-known law under certain conditions, such that the entire amount of energy is confined and stored in a spherical region of finite dimensions due to its own gravity. The reason for the transformation is the enormous pressures that exist inside the neutron star. We could say that an "energetic black hole" is a bubble of energy trapped in its own gravity. This is the main idea of this short article.
THE PUNCTUAL BLACK HOLE
The formation of black holes, as usually described by cosmologists, is explained as the collapse of a very massive neutron star that cannot stop its contraction due to the Pauli exclusion principle applied to its neutrons and therefore gravity continues to compress the star. Since no physical phenomenon is known that is capable of stopping this situation, it is postulated that the star continues to collapse until it becomes a "singularity" of zero dimensions, but conserving all its mass. Nothing is known about the singularity and the black hole itself is defined as an imaginary sphere centered on the singularity, on whose surface the escape velocity is equal to that of light. The radius of this sphere is called the "Schwarzschild radius" and is proportional to the mass of the neutron star from which it comes. This sphere would be, for all intents and purposes, the black hole with its mass and size. This explanation, based on an interpretation of a solution to Einstein's equations, seems inadequate or at least incomplete, because the concept of singularity only has a mathematical meaning, not a physical one. It would therefore be interesting to try to find some physical phenomenon capable of finally stopping the collapse of a neutron star into a black hole.
THE MATERIAL BLACK HOLE
We might think that when the neutron star collapsed beyond the Pauli limit, it might reach a new and unknown state of aggregation of matter of very high density, which for some reason resisted the collapse and so the star would stabilize to become an extremely dense and hot material body that would be the black hole. In this case, the Schwarzschild radius could be either equal to the radius of the material body, since it would be its surface from which the internal radiation could not escape, or it could be greater, as in the case of the singularity. We could thus define a black hole as a star whose Schwarzschild radius is greater than its own radius.
The description of this type of black hole and its generation is also unsatisfactory in this case, because the superdense material from which this star would be formed is not known, nor is the cause that would stop the collapse, although this type of black hole could also be described as a solution to Einstein's equations.
THE ENERGETIC BLACK HOLE
In the search for some other physical phenomenon that could constitute a limit for the contraction of the neutron star, perhaps the constancy of the speed of light could be that limit if we admit that the entire star could be converted into radiant energy. Energy itself has gravity, and if for some reason a region of space contains a sufficiently large amount of radiation, its own gravity could prevent that energy from escaping from the region.
To do this, we introduce the conjecture that the enormous pressure in the center of the star could annihilate the neutrons and somehow initiate the conversion of these neutrons (or of the central matter of the star) into energy. If this were true, this conversion would begin in the core of the star and would tend to expand and compress the outermost layers, so that the conversion would spread rapidly throughout the star from the center to the periphery and a supernova-type explosion would occur, releasing all the energy from the conversion of the total mass of the star. But if the initial neutron star were sufficiently massive, then perhaps this conversion of its core into energy could be slower and controlled by a dynamic equilibrium between the expansion of the core and the compression due to the gravity of the outer layers. During this equilibrium, the central zone of the star would gain energy and grow, while the outer layers would lose mass and decrease. But the central energy also has gravity, which increases progressively as the gravity of the outer zone decreases. Therefore, finally the entire star would be converted into a cloud of radiant energy trapped by its own gravity, and its size and shape would necessarily be determined by the Schwarzschild radius, that is, the radiation could not exceed that distance where the escape velocity is limited even for light.
But let us also consider that electromagnetic radiation always propagates at the constant speed of light, both inside and outside the cloud. So why can gravity prevent radiation from passing through the surface of the cloud and escaping to the outside? In other words: how does the gravity of the cloud itself affect the internal radiation so that it cannot escape? The answer can only be an extreme gravitational redshift. At the surface of the cloud, gravity causes any frequency to be cancelled and the radiation disappears to the outside. However, the conservation of energy inside the cloud requires that the waves do not disappear inside. This suggests that they are reflected at the inner surface and recover their initial frequency. In this way, the cloud conserves its energy and radiation pressure without being extinguished and becomes a stable and permanent object. This cloud-shaped object that does not radiate energy, has finite dimensions and maintains within itself a radiation pressure and a temperature of very high values would be what we call an "energetic black hole."
THE BLACK BODY
In general, the characteristics of black holes are similar to those of black bodies, except that there is no external radiation in the former due to their extreme gravity. But both completely absorb any radiation that falls on them and can be represented by a closed cavity with a uniform density of electromagnetic energy inside, so we could say that black holes are black bodies with a strong gravitational field that prevents their radiation as a black body.
RELATIONSHIP WITH OTHER OBJECTS
At relatively large distances from a black hole, where Newton's laws apply and the escape velocity is small, a black hole behaves like any star. Thus, for example, if the Sun were replaced by a black hole of equal mass, the movement of the planets would not change, although the entire solar system would be darkened and would not receive any heat or radiation. But at short distances from a black hole where the gravitational field is very strong and the speeds of fall are close to the value of the speed of light, the relationships with other objects must be analyzed according to relativistic laws and this is not easy.
The mysterious nature of black holes poses strange situations. For example: What happens when a small material object falls into a black hole?
In principle, the answer is that the object passes through the Schwarzschild sphere and is absorbed and integrated by the black hole, increasing its mass. However, it is unknown how it is absorbed and integrated. In the case of a punctual black hole, the object would have to change shape in order to enter the singularity. In a material black hole, both objects collapse and merge into a single body. And in the case of an energetic black hole, the object can probably be converted into energy by entering the cloud.
Another curious case is when the object falling on the black hole is much larger than the black hole, but has a much lower mass. This would be the case of the Earth falling on a black hole whose mass was equal to the mass of the Sun. The Schwarzschild radius of a black hole of one solar mass is 3 km. The ratio of diameters between the Earth and this black hole is 2,124 times in favor of the Earth. However, the ratio of masses is 330,000 times in favor of the black hole. What would happen in the collision, that is, upon contact between the Earth's surface and the surface of the Schwarzschild sphere? In my opinion, I see two possibilities, both of them extravagant:
A) the Earth is deformed and thinned by tidal forces as it approaches the black hole and after entering the Schwarzschild sphere it becomes even thinner until it reaches the singularity, which completely swallows up the Earth's mass.
B) Given the extremely high speed of the collision and the large differences in size and mass, the black hole penetrates the Earth close to its centre and from there absorbs it.
What happens when two black holes collide? In the case of a punctual black hole (official version), the collision is actually the contact of the two Schwarzschild spheres. From that moment on, both spheres merge until the two singularities coincide and the resulting black hole has a mass equal to the sum of the two previous masses. In the case of two material black holes, the two bodies would merge into one and the collision would take place according to relativistic physical laws taking into account tidal forces and high velocities.
Finally, in the case of two energetic black holes, it seems clear that both energetic clouds could mix and merge into a larger one.
DATA (taken from Wikipedia)
Mass of the Sun: 2xE30 kg
Possible range of neutron star masses: between 1.3 and 2.1 solar masses
Mass of black holes:
- BH of 1.3 solar masses: 2.6xE30 kg
- BH of 2.1 solar masses: 4.2xE30 kg
Light speed c=3xE8 m/s
Squared = c^2=9xE16 m^2/s^2
Black hole equivalent energies (e=mc^2):
- BH of 1.3 solar masses: 2.3xE47 J
- BH of 2.1 solar masses: 3.8xE47 J
G=6.67xE-11 Nm^2/kg^2
Black hole Schwarzschild radii (r= 2Gm/c^2)
- Sun: 3 km
- BH of 1.3 solar masses: 3.9 km
- BH of 2.1 solar masses: 6.3 km
Black hole volumes: (4/3)x(PI)x(Radio_Schw.)^3
- BH of 1.3 solar masses: 2.5xE11 m^3
- BH of 2.1 solar masses: 1.0xE12 m^3
What is the pressure inside a black hole? The general expression for pressure is
p = force/surface,
and in a closed space
p = energy/volume.
Therefore, in the case of a black hole of 2.1 solar masses we have:
Internal pressure of black holes (p=e/v);
-BH of 2.1 solar masses: p = 3.8xE47/1.0xE12= 3.8xE35 Pa.
As a term of comparison, we have that the estimated radiation pressure in the core of the Sun is 2.65xE16 Pa. That is, it is lower by approximately 20 orders of magnitude.
CONCLUSION
Black holes are strange bodies unknown to science because their genesis is not yet well explained. The concept of "singularity" is accepted without problems by cosmologists, but it seems like an invention to describe an impossible entity: a mathematical point endowed with physical mass. If, on the other hand, a black hole is a material object of very high density, we do not know the nature of the material it is made of. Finally, if it consists of an immaterial bubble of radiant energy confined by its own gravity, we do not know the process of formation of that bubble from a neutron star. For all this we can say that black holes remain fascinating objects of unknown nature.
R. Chamón Cobos.
October 2024.