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European Journal of Applied Sciences – Vol. 11, No. 1
Publication Date: February 25, 2023
DOI:10.14738/aivp.111.13922. Cruz Gomez, J. M. (2023). Through the Review of Hydrogen, Neutrons and Black Holes, An Explanation of Black Matter as
Constituted Only by Neutron Stars and Black Holes is Proposed. European Journal of Applied Sciences, Vol - 11(1). 419-431.
Services for Science and Education – United Kingdom
Through the Review of Hydrogen, Neutrons and Black
Holes, An Explanation of Black Matter as Constituted
Only by Neutron Stars and Black Holes is Proposed.
Cruz Gomez, Javier M.
Department of Chemical Engineering,
Faculty of Chemistry, Universidad Nacional Autónoma de México, México
ABSTRACT
Using the diameters of a hydrogen molecule, H2, a hydrogen atom, H, and of a
neutron, N, it is quantified how the densities increase: a). When the empty space
between the molecules of H2 at standard conditions of temperature and pressure is
eliminated to form solid H2, and b). When the empty space between the electrons
and nuclei of an atom is eliminated to form only neutrons. Using the mass of an
average neutron star of 1.8 solar masses it is shown how heavy this matter is, due
to its high density of 6.46x1014 g/cc. Using the mass and volume of the quarks and
of the quarks and gluons inside the neutron it is explored where the mass of a 5
solar mass black hole is located inside the volume delimited by the Schwarzschild
radius. Next it is proposed the theory that what is called dark matter is a high
number of neutron stars and black holes, equivalent to one of any of them per about
each star in the actual universe.
Keywords: Neutrons, stars, neutron stars, black holes, galaxies, universe.
INTRODUCTION
The article begins recapitulating some basic information like the size, densities, existence and
characteristics of hydrogen molecules, hydrogen atoms, neutrons, protons, electrons, and
quarks. Then it is made a comparison between a neutron star and a black hole. Knowing that
the number of black holes is big, and they continue forming, it is postulated a theory that the
black matter in the universe is composed mainly of neutron stars and black holes distributed
in the galaxies, and in the empty space of the universe. Since nobody knows what the black
matter is, it is calculated the equivalent number of black holes that should have been formed in
the Universe, to substitute all the black matter for black holes and/or neutron stars.
DIAMETER OF SOME PARTICLES
In Table 1 it is shown the particle diameter of 6 particles. Even though some authors give
slightly different values for these diameters, there are used the given values throughout the
article.
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Table 1, Diameter of 6 particles.
Particle Diameter, cm Diameter, m
A H2 molecule at STP (1) 2.89x10-8 2.89x10-10
A hydrogen atom (2) 1.20x10-8 1.20×10-10
A neutron (3) 1.7×10−13 1.7×10−15
A proton (4) 1.7x10-13 1.7x10-15
An electron (5) 4x10-16 4x10-18
A quark (6) 1x10-16 1x10-18
Now it will be obtained the densities of these particles and make comments about them.
DENSITY OF MOLECULAR HYDROGEN
If we consider that 1 mole of molecular hydrogen, H2, has at standard conditions of
temperature and pressure (STP (7)), a weight of 2.0 grams and a volume of 22,400 cc, then the
H2 density, d_H2, is:
d_H2 = 2.0 g/2.24x104 cc= 8.93x10-5 g/cc at STP...... (1)
The STP are: 0.0 Celsius degrees and 1.0 atmosphere (atm) of pressure.
The volume of a H2 molecule, v_H2, is:
v_H2 = (4 ∏/3) (r)3 = (4 ∏/3) (0.5x2.89x10-8 cm)3
= 12.64x10-24 cc....... (2)
The volume of an Avogadro number of hydrogen molecules, v_anh2, is:
v_anh2 = (6.022x1023 molecules) (12.64x10-24 cc/molecule)
= 7.61 cc = 0.00761 liters...... (3)
An example of the reduction in volume, from 22,400 cc to about 7.61 cc, is when H2 is cool down
from 273.1 K (0 °C) to a liquefying temperature of 20.2 K and then to 14 K when the H2
solidifies. Solid H2 is equivalent to having the H2 molecules attached one to the other.
The volume of a sample of 1 mole of molecular H2 at STP is mainly vacuum, since its molecules
are using only 0.034 % (0.00761 liters) of the total volume, 22.4 liters, and the empty volume
is 99.966 % of that volume.
With the weight of one mole of H2, the density of the solidified hydrogen molecules, d_shm,
would be:
d_shm = (2 g)/ (7.61 cc) = 0.263 g/cc
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Cruz Gomez, J. M. (2023). Through the Review of Hydrogen, Neutrons and Black Holes, An Explanation of Black Matter as Constituted Only by
Neutron Stars and Black Holes is Proposed. European Journal of Applied Sciences, Vol - 11(1). 419-431.
URL: http://dx.doi.org/10.14738/aivp.111.13922
Experimentally it has been determined (8) that solid hydrogen has a density of 0.086 g/cm3.
The density of a sample of a mole of molecular H2 increases from 8.93x10-5 g/cc, when it is a
gas at STP, to about 0.086 g/cc when it is converted into solid H2.
DENSITY OF HYDROGEN ATOMS PACKED TOGETHER
Now it will be obtained the hydrogen atom volume, v_ha, in the same way as it was made for
molecular hydrogen:
v_ha = (4 ∏/3) (0.5x1.2x10-8 cm)3 = 9.05x10-25 cc
= 9.05x10-28 liters...... (3)
The volume of an Avogadro number of hydrogen atoms, v_anha, is:
v_anha = (6.022x1023 molecules) (9.05x10-25 cc/molecule)
= 5.45x10-1 cc...... (4)
Since 1 mole of hydrogen atoms weighs about 1 gram, the density of hydrogen atoms, d_ha, if it
were possible to bring each hydrogen atom together touching the 6 neighbors, would be about:
d_ha = (1 g)/ (5.45x10-1 cc) = 1.835 g/cc...... (5)
Although in a normal laboratory it is not possible to have hydrogen atoms stuck together, it is
mentioned that in the Sun there are conditions of temperature, pressure, and mainly
gravitational force, that allows the Sun mass to be at a density of 1.41 g/cc, almost the calculated
density of hydrogen atoms stuck together, d_ha. The Sun physical conditions (9) are: a).
Composition: 73 % hydrogen, 25% helium and 2% of other heavier elements like carbon,
oxygen, nitrogen, etc., b) Temperatures: The Sun core is at 15 million K and its surface at 5,778
K, c). Forces in equilibrium: The force that keeps the atoms almost stuck is that of the gravity
generated by a solar mass that is 330,000 times greater than the mass of the earth, and the force
that tends to separate them is the flow of energy that leaves the center of the Sun(10) due to
the fusion nuclear reactions, happening in the core of the Sun, whereby hydrogen nuclei are
converted to helium nuclei.
MASS, VOLUME, DIAMETER, AND DENSITY OF NEUTRONS PACKED TOGETHER
Next it is exposed the properties of neutrons, based in 1 mole, equivalent to one gram of
neutrons, and then based on the mass of an average neutron star.
A). Density and Volume of Neutrons Packed Together, Based on 1 Mole.
The volume occupied by a neutron, v_ne, is:
v_ne = (4 ∏/3) (0.5x1.7×10−13 cm)3 = 2.57x10-39 cc....... (6)
One mole of neutrons will have the volume, v_mn, of:
v_mn = (6.022x1023 neutrons) (2.57x10-39 cc/neutron)
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= 1.548x10-15 cc...... (7)
With the volume of one mole of neutrons packed together, v_mn, and its weight of about 1 gram,
is obtained the density of neutrons, d_ne, packed together:
d_ne = (1 g)/ (1.548×10−15 cc) = 6.46x1014 g/cc...... (8)
This density, d_ne, is big since the space between molecules and the space between the nucleus
and the electrons of an atom have been eliminated.
B). Mass, Volume, and Diameter of an Average Neutron Star
In the Universe the neutron stars are a clear example of what are the bodies made with packed
neutrons. A neutron star (11) is the remaining collapsed core of an exploded, at the end of its
life, giant massive star, which had a total mass between 10 and 25 solar masses (M☉). The
remaining core has a mass between 1.4 M☉ and 2.16 M☉.
Now it will be calculated the mass, m_ns, volume, v_ns, and diameter, d_ns, of a hypothetical
neutron star with a mass of 1.8 M☉, equivalent to the average weight of neutron stars.
The mass, m_ns, of 1.8 M☉, knowing that the weight of 1 M☉ = 2x1033 g, is:
m_ns = (1.8 M☉) (2x1033 g/M☉) = 3.6x1033 g...... (9)
Using the density of neutrons obtained in equation (8), the volume of this neutron star, v_ns, is:
v_ns = m_ns/d_ne = (3.6x1033 g)/ (6.46x1014 g/cc) = 5.573x1018 cc
= (5.573x1018 cc)/ (1x106 cc/m3) = 5.573x1012 m3.......(10)
The diameter of this neutron star, d_ns, (calculated from the radius, r_ns, of the formula for the
volume of a sphere) is:
r_ns = ((3 v_ns)/(4x∏))1/3 = ((3x5.573x1012 m3)/(4x∏))1/3
= 1.1x104 m...... (11)
d_ns = (2)(r_ns) = (2)(1.1x104 m) = 2.2x104 m = 22.0 K (12)
It has been reported that a typical neutron star diameter, d_ns, is of about 20 km (12), quite
close to the numerical value obtained in Equation (12), even though its physical conditions are
special: a). Surface temperature around 106 kelvins, b). Gravitational field at a neutron star's
surface of around 2.0×1012 m/s2, which is 2×1011 times stronger than that on Earth, and c). It
is believed that in the neutron star core there is a quark gluon plasma.
From the previous results it can be commented that: a). The diameter of a neutron star is
equivalent to that of an average city, which is, very small compared to its great mass, and b).
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Cruz Gomez, J. M. (2023). Through the Review of Hydrogen, Neutrons and Black Holes, An Explanation of Black Matter as Constituted Only by
Neutron Stars and Black Holes is Proposed. European Journal of Applied Sciences, Vol - 11(1). 419-431.
URL: http://dx.doi.org/10.14738/aivp.111.13922
Just to have an idea of how heavy a piece of neutron star volume is, it is obtained the weight of
a 5 cc teaspoon of neutron star material:
Weight of a 5 cc teaspoon = (5 cc)(6.46x1014 g/cc) = 3.23x1015 g
= 3.23x109 tons = 3.23 billion tons...... (13)
It has been calculated that the total mass of neutron stars is not smaller than the Chandrasekhar
limit (13) of 1.39 M☉. Since if they have a mass smaller than 1.39 M☉, they will be converted
into a white dwarf. Also, the neutron stars are not bigger than the Tolman–Oppenheimer–
Volkoff limit (14) which is of about 2.16 M☉. Since if they have a mass greater than 2.16 M☉
they will collapse into a black hole.
DENSITY OF THE QUARKS-GLUONS PACKED TOGETHER INTO A BLACK HOLE
According to Lincoln, D. in Quantum field theory (15), “In modern physics, one can picture the
subatomic particles as localized vibrations in a field”. Quarks and gluons are the building blocks
of protons and neutrons. The current understanding of scientists is that quarks and gluons are
indivisible and inseparable—they cannot be broken down into smaller components. The only
way to manipulate these particles is to create a state of matter known as quark-gluon plasma.
In this plasma, the density and temperature are so high that protons and neutrons melt into a
soup of quarks and gluons. This type of soup once permeated the entire universe until a few
fractions of a second after the beginning of the universe, when the universe cooled enough to
led quarks and gluons froze into protons and neutrons.
To have a discussion and make some comparisons between neutrons, quarks, and gluons the
following concepts, for an imaginary body of 5 M☉, will be developed: a). A neutron star, b). A
black hole, c). A quark and gluon mass and d). Finally give some comments about the location
of the mass that makes up a neutron star.
A Neutron Star
The radius and diameter of an assumed neutron star, formed at least instantaneously when the
remaining of an exploded star, happens to be of 5 M☉, r_5sm, is calculated from its mass,
m_5sm, and its volume, v_5sm, as follows:
m_5sm = (5 M☉) (2x1033 g/M☉) = 1.0x1034 g...... (14)
Next it is used the density of neutrons, d_ne, obtained in equation (8) to get the volume, v_5:
v_5sm = (m_5sm)/(d_ne) = (1.0x1034 g)/(6.46x1014 g/cc)
= 1.548x1019 cc = 1.548x1013 m3...... (15)
r_5sm = ((3 x v_5sm)/(4 ∏))1/3 = ((3x1.548x1013 m3)/(4 ∏))1/3
= 1.546x104 m = 15.46 Km ≈ 15.5 km...... (16)
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Diameter of the 5 M☉ neutron star, d_5sm, is:
d_5sm = 2x15.5 km = 31.0 Km...... (17)
This supposed 5 M☉ neutron star can only exist instantaneously since, due to the force of
gravity of its great mass, it would continue shrinking until it becomes a black hole.
A Black Hole
A black hole (BH) is the remaining collapsed core of an exploded, at the end of its life, supergiant
massive star, which had a total mass greater than 25 solar masses. The mass of a stellar BH is
greater than the Tolman–Oppenheimer–Volkoff limit. We will continue in this example with a
BH mass of 5.0 solar masses, which can be visualized as an average or commonly formed stellar
black hole. It is not known the volume in which the BH mass is contained, but everybody agrees
that the mass is inside the Event Horizon radius, r_eh, also called the Schwarzschild radius (16),
and it is the radius of an imaginary sphere at which the BH escape velocity is equal to the speed
of light. This radius can be calculated by assuming that it is located at the point in which the
centripetal force, [Fc = (m v2)/r], is equal to the gravitational force, [Fg = (G M m)/r2]. By taking
v = c, the speed of light, equating Fc with Fg, and solving the equation for the radius, r, we get:
r = (GM)/c2...... (18)
Where:
G = 6.67x10-11 m3/kg-s2, the Newton ́s gravity constant (19)
M = The mass of 5.0 M☉ = 5x2x1030 Kg = 1.0x1031 Kg... (20)
c = The speed of light = 3x108 m/s...... (21)
r_eh = (6.67x10-11 m3/kg-s2) (1.0x1031 Kg)/(3x108 m/s)2
= 0.741x104 m = 7.41 km ≈ 7.4 km...... (22)
“The event horizon radius (17) (proportional to the mass) is very small, only 7.4 kilometers for
a non-spinning black hole with the mass of 5 Suns”. Since the BHs mass is greater than in
neutron stars, it also exerts a greater gravity.
Next, it is obtained the volume, v_bh, for a 5.0 M☉ BH as:
v_bh = (4 ∏/3) (0.741x104 m)3 = 1.70x1012 m3...... (23)
Quarks and Gluons Masses
It is known, see Table 1, that the diameter of a quark is 1,700 times smaller than the diameter
of a proton or a neutron, but it is not possible to reduce the volume of neutrons to that of quarks,
since attached to the quarks there are gluons with which they interact. What is known is that
at a temperature of 1.66×1012 K it is possible to produce or form a quark-gluon plasma (18).
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Cruz Gomez, J. M. (2023). Through the Review of Hydrogen, Neutrons and Black Holes, An Explanation of Black Matter as Constituted Only by
Neutron Stars and Black Holes is Proposed. European Journal of Applied Sciences, Vol - 11(1). 419-431.
URL: http://dx.doi.org/10.14738/aivp.111.13922
Experimentally, this so high temperature can be accomplished by colliding two large nuclei at
high energy. At the Conseil Européen pour la Recherche Nucléaire (CERN) gold and lead nuclei
have been used for such collisions. For a real BH center, the temperature is high, but we do not
know how close to the quark-gluon-plasma it is. On the other side it is also known that the
temperature of the BH event horizon surface is only of 2.7 K. An interpretation of this is that
the high BH gravity keeps near the center even the heat waves.
Next it will be obtained the mass, volume and density of a quark and gluon mass sample of 5
M☉.
By considering that the average quark diameter is 1x10-16 cm, see Table 1, then the volume of
an average quark, v_aq; is:
v_aq = (4 ∏/3)(0.5x1x10-16 cm)3 = 2.094x10-48 cc...... (24)
The volume of 3 moles of quarks, v_3mq, is:
v_3mq = (3)(6.022x1023)(2.094x10-48 cc) = 3.7837x10-24 cc. (25)
Since the total mass of a mole of neutrons or protons, each having 3 quarks, is about 1 gram and
the gluons have cero mass, it could be said that in the molar volume of 3 quarks, v_3mq, is
contained the hole mass of about 1 gram (Even though in the Standard Model of elementary
particles (19) it is mentioned a much smaller mass for the Up and Down quarks.). The volume
of 5 M☉ of quarks-gluons, v_qgbh, can be calculated from the volume of 1 gram of mater
subjected to the conditions of a black hole, as follows:
v_qgbh = (5 M☉) (2x1033 g/M☉)(3.787x10-24 cc/g)
= 3.787x1010 cc...... (26)
The radius of the quarks-gluons black hole spherical volume, r_qgbh, is:
r_qgbh = ((3 v_qgbh)/(4x∏))1/3 = ((3x3.787x1010 cc)/(4x∏))1/3
= 2.083x103 cm = 20.83 m = 0.02083 km...... (27)
This radius is certainly very small.
Where is the Mass of the Quarks-Gluons, That Make Up the Protons or Neutrons, That
Finally were Converted into A Black Hole?
About the fact that the event horizon radius (r_eh ≈ 7.4 km) is smaller than the radius of an
assumed neutron star (r_10sm ≈ 15.5 km) and much bigger than the quarks-gluons BH
spherical volume (r_qgbh ≈ 0.02083 km), at least two explanations have been given. The first
of these goes to the extreme, by saying that the BH ́s mass continues to shrink until it is confined
within a point of infinite density (20). This point is also called a singularity which is located at
the BH center. This explanation might not hold true for these parts of the universe. The second
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explanation (21) is that the 5 M☉ mass of the quarks-gluons did contract, but only to form a
quark-gluon plasma. It is not known what the radius of this plasma is, but it is assumed that it
has a finite radius, not that of cero from a point, but a value smaller than the Schwarzschild
radius. It could be the radius of the quarks-gluons black hole calculated in Equation (27). For
the example being analyzed, the BH mass with a total mass of 5 M☉ will have a radius of less
than the BH event horizon radius of 7.4 km. But, since it is not possible to get any signal from
inside the BH, then it is not possible to know anything of the interior of the BH.
With respect to the existence of the BHs it has been commented that although only a couple
dozen BHs have been found in the Milky Way so far, there are thought to be hundreds of
millions, most of them are solitary, do not cause emission of radiation (22), and they are
detectable only by gravitational lensing.
With the calculated BH Schwarzschild radius, a hypothetical superficial boundary sphere is
formed. If an object crosses it, the object will be swallowed by the gravity force into the black
hole. It will not be possible to go out since nothing can move at a speed greater than the speed
of light.
TWO EXAMPLES OF THE SUPERMASSIVE BLACK HOLES
It is known and accepted that at the center of each galaxy there is a supermassive BH, around
which the galaxy stars move. Each of these supermassive BHs was formed, during the first
billion years of the Universe existence, by merging surrounding mass of stars and millions to
billions stellar BHs or neutron stars. Some of the BH that were formed during this time could
be the primordial (23) BHs; however, their existence has not been proven and remains
hypothetical.
The Image of Sagittarius A* Black Hole
At the center of our own Milky Way galaxy there is a supermassive black hole (BH) named
Sagittarius A* (24), with a mass of 4.154x106 M☉. The Sagittarius A* Schwarzschild radius is
calculated to be of 5.92x106 Km. (Around 6 million kilometers). The scientific community that
works with the Event Horizon Telescope, (EHT), published on May 12, 2022, the picture of
Sagittarius A* BH, located at 25,673 light years from the Earth. It is a dead, inert, quiet BH and
smaller than M87* BH that will be described next.
First-Ever Image of a Black Hole Published by the Event Horizon Telescope
Collaboration. April 10, 2019
In a virtual media conference, Laurent Raymond Loinard, a researcher at the Institute of Radio
Astronomy and Astrophysics (IRAyA) of UNAM, Morelia campus (25), presented an image in
polarized light of M87*, which is more than 1,500 times more massive than Sagittarius A*. It is
a supermassive BH at the center of the galaxy M87, located at 53 million light years from the
Earth. Figure 1 shows (26) the first real image produced, in April 2019, of a BH by the
international collaboration of the EHT.
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Cruz Gomez, J. M. (2023). Through the Review of Hydrogen, Neutrons and Black Holes, An Explanation of Black Matter as Constituted Only by
Neutron Stars and Black Holes is Proposed. European Journal of Applied Sciences, Vol - 11(1). 419-431.
URL: http://dx.doi.org/10.14738/aivp.111.13922
Figure 1.
M87* is an active galactic nucleus (AGN). The non-stellar radiation from an AGN is theorized to
result from the accretion of matter by this supermassive BH at the center of its host galaxy.
WHAT IS CALLED BLACK MATTER, IT IS PROPOSED IN THIS ARTICLE THAT IN REALITY,
IS A LARGE BUT PRECISE NUMBER OF KNOWN MATTER, NEUTRON STARS AND BLACK
HOLES, DISTRIBUTED THROUGHOUT THE UNIVERSE
In every galaxy of the universe there may well be hundreds of millions of BHs like in the Milky
Way. It is also known that at the center of each galaxy there is a supermassive BH, which was
formed by the merger of millions or billions (27) of stars, neutron stars and mainly of stellar
BH. Next, the equivalent number of stellar BHs that should exist in the universe to constitute
the so-called dark matter of the universe will be calculated.
It is known that the diameter of the visible universe is of 9.3x1010 light years (28), its volume
is of 3.5655x1080 m3, and its total mass is of 3.53x1054 Kg. This mass is composed (29) of
4.6% of visible matter, 24.0% of black matter and the remaining 71.4% of black energy. This
means that the total black matter, m_tbm, in the universe is:
m_tbm = (0.24) (3.53x1054 Kg) = 8.472x1053 Kg...... (28)
It will be assumed that the average mass of a BH is 5.0 M☉, and the mass of this typical BH, M,
will be taken as that of Equation (20) of 1.0x1031 Kg. Now it will be calculated the number of
typical stellar BHs, n_sbh, necessary to make all the universe’s black mater:
n_sbh = (m_tbm/M) = (8.472x1053 Kg)/ (1.0x1031 Kg)
= 8.472x1022...... (29)
The real number of stellar black holes, n_sbh, is smaller than the calculated in Equation (29),
since some of these stellar black holes were merged to form the supermassive black holes that
exist at the center of each of the 2x1011 galaxies that constitute the universe, whose mass is
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between several million to several billion of solar masses (30). Also, the equivalent mass of
many of the calculated BHs is the mass of neutron stars that are inside or outside the galaxies.
Now the number, n_sbh, will be compared with the number of stars in the universe, n_su. Since
the number of stars in an average galaxy, like the Milky Way, is of about four hundred thousand
million (31) (4x1011 stars/galaxy) and the number of galaxies in the universe is of two hundred
thousand million (32) (2x1011 galaxies/universe), then the total number of stars in the
universe is:
n_su = (4x1011 stars/galaxy) (2x1011 galaxies/universe)
= 8x1022 stars in the universe ...... (30)
By comparing the number of stellar BHs, from Equation (29) with the total number of stars,
from Equation (30), it can be concluded that in the visible universe, up to now, have been
formed the equivalent of one BH per each now existing star. Even though the smaller ones
remain as neutron stars, and some were merged to form supermassive black holes. The black
holes, with a variety of masses around the 5 M☉, are in between the stars of galaxies and some
others in the empty space between galaxies. And, as it was said above, most of them are solitary
and do not cause emission of radiation.
The existence of many stellar BHs and neutron stars in between the galaxy’s stars can explain
a). The special movement of the stars around its black hole and b). The movement of the
galaxies around a cluster.
a). The particularity with the movement of the stars around the center of their galaxy is that as
the distance from a particular star-A to its center is bigger, the velocity of the star should be
slower. But the velocity of that star-A remains constant (33). The explanation for that is that
there is more mass, than the mass of the centered black hole, and that of the stars and dust
inside the radius of star-A.
b). Something similar happens with the galaxies that make up a cluster. It is observed that with
the speed at which the galaxies move, the cluster could not be kept together. The explanation
given is that there is much more mass than that of the galaxies that are observed. In the case of
the Coma Cluster (34), it is said that the amount of dark matter can be up to 90% of the total
mass of the Cluster.
The extra mass between the stars of a galaxy and between the galaxies of a cluster has been
called black matter. But now in this article it is proposed that what is called black matter is the
equivalent mass of BHs (35), approximately one BH for each visible star, with a radius of all the
possible sizes, distributed aleatorily between the galaxy stars and a good number of them
substituted by the equivalent mass of the existing neutron stars.
In the case of the Andromeda galaxy, it has been reported (36) that it has a total mass between
0.7 and 2.5 trillion M☉. If it is taken as the total mass 2.4x1012 M☉, and as the total number of
stars in the galaxy 400 thousand millions. Then it is possible to conclude that the mass of the
stars is of 0.40x1012 M☉, and there is an excess mass of 2.0x1012 M☉ to make about one BH
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Cruz Gomez, J. M. (2023). Through the Review of Hydrogen, Neutrons and Black Holes, An Explanation of Black Matter as Constituted Only by
Neutron Stars and Black Holes is Proposed. European Journal of Applied Sciences, Vol - 11(1). 419-431.
URL: http://dx.doi.org/10.14738/aivp.111.13922
of an average mass of 5 M☉, per each star, i. e. 0.40 x1012 BHs. Even though some BHs, have
been merged to form more massive BHs, and millions to billions have been merged to form the
supermassive BHs that exist at the center of each galaxy. Also, the equivalent mass of many of
the calculated BHs is the mass of neutron stars that are inside the galaxy.
DISCUSSION AND CONCLUSIONS
The huge mass concentrated into the sphere with the relatively small Schwarzschild radius of
a black hole is something that can have more consequences and interpretations. In this article
it was taken 5 M☉ as the average mass of the stellar BHs and that some of them are substituted
by neutron stars. Later, it can be analyzed a big enough sample of the many BHs that are been
discovered and neutron stars to determine a new average mass value to obtain a better value
for the number of them in the Universe. All these BHs and neutron stars started to form a few
hundred million years after the beginning of the Universe to accumulate, during the life of the
Universe, the equivalent mass of what is called black matter.
No one knows what dark matter really is, but enough is known about BHs and neutron stars to
make the proposal for this article: what causes the effects of the black matter is a big amount of
radiationless stellar BHs and neutron stars distributed throughout the universe, and specially
between the stars of the galaxies. It was calculated that the equivalent number of BHs is about
the same as the number of stars in the universe. If it were possible to measure for several
galaxies their total mass (By gravitational lens (37) for example) and the number of stars they
contain (By any suitable observational technique), then it should be possible to have another
number for the equivalent number of BHs that the galaxies should contain and compared it with
the number of BHs calculated in this article.
About the number of galaxies in the Universe that is used in the article some people think that,
as more observations are made, the number my increase. With respect to the percentage of
black matter the number varies with the author. But making the adjustments in the number of
galaxies and in the black matter percentage, the overall idea of this article does not change.
Regarding the numbers and conclusions, for the Andromeda galaxy, about the total mass,
number of stars and BHs it contains, which were mentioned in section 8 of this article, it is
accepted that more observational data is needed to obtain more precise numbers and
conclusions about this galaxy. Also, it is necessary to have similar data about the total mass and
the number of its stars from more galaxies, to obtain a better number for the ratio of stars to
BHs in the universe.
If you, the reader of this article, have any comments on the theory proposed here, I will be very
grateful if you send them to the author ́s email.
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