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With recent detection of black hole mergers by LIGO, the 'Black Holes' and 'Neutron Stars' have become common house-hold names, albeit fanciful names in public domain. However, for the scientific community black holes are the ultimate paradoxes of nature. The claimed observations of black hole mergers are in fact interpretations of certain observations under the spacetime model of Relativity. These interpretations can change significantly with the change in operating model of the phenomenon. A black hole is believed to be a ‘region of spacetime’ exhibiting such strong gravitational effects that nothing, not even light can escape from it. We demonstrate in this paper that this conviction is based on erroneous derivation for the gravitational redshift and the correct derivation shows that a photon cannot be prevented from escaping a gravitating body of any mass and size. Due to erroneous depiction of spacetime as a physical entity in GR, a mathematical singularity predicted by Schwarzschild metric solution of EFE has been projected as a physical possibility in the form of Black Holes. To strengthen the physical basis of Black Hole creation, the observations of Super Nova explosions are being interpreted under core collapse models. The core collapse models are now regarded as the physical foundation of Black Holes and Neutron stars. In this paper we have established the invalidity of current core collapse models on the grounds of treating electrons, ions and nuclei as non-interacting particles and using kinetic theory of gases for analyzing compressive stresses in solid iron core.
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Applied Physics Research; Vol. 11, No. 4; 2019
ISSN 1916-9639 E-ISSN 1916-9647
Published by Canadian Center of Science and Education
16
Black Holes are a Mathematical Fantasy, not a Physical Reality
Gurcharn S. Sandhu1
1 Independent Researcher, India
Correspondence: Gurcharn S. Sandhu, #48, Sector 61, Mohali, Punjab – 160062, India. Tel: 91-981-462-2204.
E-mail: gurcharn.sandhu@gmail.com
Received: June 8, 2019 Accepted: June 18, 2019 Online Published: July 15, 2019
doi:10.5539/apr.v11n4p16 URL: http://dx.doi.org/10.5539/apr.v11n4p16
Abstract
With recent detection of black hole mergers by LIGO, the 'Black Holes' and 'Neutron Stars' have become common
house-hold names, albeit fanciful names in public domain. However, for the scientific community black holes are
the ultimate paradoxes of nature. The claimed observations of black hole mergers are in fact interpretations of
certain observations under the spacetime model of Relativity. These interpretations can change significantly with
the change in operating model of the phenomenon. A black hole is believed to be a ‘region of spacetime’ exhibiting
such strong gravitational effects that nothing, not even light can escape from it. We demonstrate in this paper that
this conviction is based on erroneous derivation for the gravitational redshift and the correct derivation shows that
a photon cannot be prevented from escaping a gravitating body of any mass and size. Due to erroneous depiction
of spacetime as a physical entity in GR, a mathematical singularity predicted by Schwarzschild metric solution of
EFE has been projected as a physical possibility in the form of Black Holes. To strengthen the physical basis of
Black Hole creation, the observations of Super Nova explosions are being interpreted under core collapse models.
The core collapse models are now regarded as the physical foundation of Black Holes and Neutron stars. In this
paper we have established the invalidity of current core collapse models on the grounds of treating electrons, ions
and nuclei as non-interacting particles and using kinetic theory of gases for analyzing compressive stresses in solid
iron core.
Keywords: Black Holes, core collapse, Neutron Star, gravitational redshift, ionic pressure, Super Nova
1. Introduction
Black holes are said to be the ultimate paradoxes of nature. A black hole is believed to be a ‘region of spacetime
exhibiting such strong gravitational effects that nothing, not even electromagnetic radiation such as light, can
escape from inside it. The general theory of relativity (GR) predicts that a sufficiently compact mass can ‘deform
spacetime’ to form a black hole. The boundary of the region from which no light can escape is called the Event
Horizon. Since long, black holes have been a mathematical curiosity; it was during the 1960s that they were
theoretically shown to be a generic prediction of GR. The discovery of neutron stars in 1967 sparked interest in
gravitationally collapsed compact objects as a possible astrophysical reality of black holes. Stellar mass black
holes are believed to form when very massive stars collapse at the end of their life cycle. After a black hole has
formed, it can continue to grow by attracting mass from its surroundings. It is believed that by absorbing nearby
stars and merging with other black holes, supermassive black holes of millions of solar masses are formed. Most
black holes are believed to emerge from the remnants of Core Collapse SuperNova explosions (CCSNe) at the end
of life cycle of large stars. Smaller stars are assumed to become dense neutron stars, which are not massive enough
to trap light (Couch, 2017).
The popular notions of black holes however, imply the 4D-spacetime to be a physical entity. The geometrical
interpretation of gravitation in General theory of Relativity (Einstein, 1916) also implies the spacetime continuum
to be a physical entity which can even be rippled, deformed and curved.
We need to distinguish between the mathematical abstract notion of coordinate space for quantification of relative
positions and the physical notion of space as the container of physical objects. The predefined notion of unit length
or scale for different coordinate axes, constitutes the metric of space for quantifying the notion of distance and
position measurements. Thus, coordinate space is a mathematical tool used for the dynamic study of physical
objects embedded in 3D Physical Space. Whereas the metric scaling property is only associated with coordinate
space, the physical properties of permittivity, permeability and intrinsic impedance are associated with physical
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space. The speed 'c' of propagation of electromagnetic disturbances is governed by the permittivity and
permeability constants associated with the physical space or vacuum. These physical properties are not correlated
with the metric tensor of the coordinate space and hence cannot represent the metric properties of the coordinate
space.
It has been analytically proved (Sandhu, 2011) that the 4D spacetime of GR is not a physical entity and hence GR
is not a theory of gravitation. Specifically, it has been shown that the popular notion of spacetime curvature when
applied to physical space, leads to incompatible deformation of space with voids and discontinuities which are
physically impossible. Popular usage of the terms region of spacetime or ripples in spacetime are highly
misleading as they convey the impression of spacetime being a physical entity whereas in reality the ‘spacetime
is just a mathematical construct in the GR model. At the center of a Black Hole, as described by general relativity,
lies a gravitational singularity’, a region where the spacetime curvature’ becomes infinite. The appearance of
singularities in general relativity is commonly perceived as signaling the breakdown of the theory. Given the
bizarre nature of black holes, it has since long been questioned (Einstein, 1939) whether such objects could actually
exist or whether they were merely pathological solutions of mathematical models. On the top of it the LIGO
collaboration announced many direct detections of gravitational waves, which are claimed to represent the unique
observations of black hole mergers.
2. Gravitational Redshift in GR
Under Newtonian theories of gravitation, only matter particles are the sources of gravitation field and only matter
particles experience gravitational attraction. However, under GR all forms of matter and energy, including the
energy of electromagnetic field, contribute towards the production of gravitation field. Hence, under GR the
electromagnetic energy of photons does get influenced by the gravitational field just like the total energy or mass
of the matter particles. That is, under GR a photon of frequency ν does experience gravitational attraction towards
a massive body of mass M, in proportion to the photon energy hν or its equivalent dynamic mass hν/c2 and hence
experience redshift while escaping from a gravitation field (Sandhu, 2017).
In GR it is believed that for extremely massive and compact bodies, whose Schwarzschild radius Rs is greater than
their physical body radius R0, their gravitational attraction will be so strong that no photon of any energy content,
emitted from radius R≤Rs will be able to escape from that body. This precisely is the notion of Black Hole in GR.
However, if a photon is emitted from the surface of a less massive body with Rs<R0 or emitted from any radius
R>Rs then that photon will be able to escape from the gravitating body but only after losing a fraction of its energy
in overcoming the gravitational pull. The reduced energy of the escaping photon is observed as its reduced
frequency and this reduction in frequency is known as gravitational redshift. The gravitational redshift is said to
be an experimentally verified phenomenon (Earman & Glymour, 1980).
In GR the quantitative relations for computing the magnitude of gravitational redshift are based on the well-known
concepts of gravitational potential. The gravitational potential (V) at a given location is the gravitational potential
energy per unit mass. Thus, at a distance r from the center of a spherically symmetric body of mass M, the
gravitational force Fg on a body of mass m is given by,
𝐹𝑔󰇛𝑟󰇜=−𝐺𝑀𝑚
𝑟2, (1)
where G is Newton’s gravitation constant. The gravitational potential V as the gravitational potential energy per
unit mass is given by,
V(r) =

𝑑𝑟
=−
(2)
It is important to note in equation (2) that in the integral of gravitational force, M and m remain constant and can
be taken out of the integral sign. Normally, when a small body of mass m is brought to a location of gravitational
potential V(r) its potential energy will be given by m.V(r), implying thereby that a gravitational interaction energy
of m.V(r) has been released from the gravitational field and converted to kinetic energy (T) of the interacting
bodies. Conservation of energy ensures that the sum of the kinetic and potential energies remains constant at all
points in the gravitational field. Therefore, if a test body of mass m with kinetic energy T1 moves from location
r1with gravitational potential V(r1) to a location r2 with gravitational potential V(r2) then the new kinetic energy T2
at location r2 will be given by the energy conservation relation,
T1 + m.V(r1) = T2 + m.V(r2) (3)
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Considering location r2 to be at infinite distance from the center of the gravitating body, where the gravitational
potential V(r2) reduces to zero by equation (2), we get the escape energy T2 as,
T
2 = T1 + m.V(r1) (4)
Now, let us replace the test body of mass m with a photon of frequency ν1 at location r1. The total energy T1 for
this photon will be hν1 and the dynamic mass or the ‘effective mass’ of the photon will be given by hν1/c2. Then
from equations (2) and (4), the escape energy T2 = hν2 of the photon will be given by,
=hν
+
.V󰇛r󰇜=hν


(5)
Or ν2
ν1=1−GM
c2r1 (6)
Equation (6) represents the standard gravitational redshift formula under the so called weak-field conditions.
However, under strong gravitation field conditions, equation (6) is modified by the Schwarzschild metric
coefficient as follows.
ν2
ν1=1−2GM
c2R0 (7)
where R0 represents the physical radius of the surface of the gravitating body of mass M. The Schwarzschild radius
Rs obtained from the Schwarzschild metric is given by,
Rs=2GM
c2 (8)
When the gravitating body is so compact that its surface radius R0 is equal to (or less than) the Schwarzschild
radius Rs then the right-hand side of equation (7) will vanish leading to zero energy or zero value of frequency ν2
of the escaped photon. That precisely is the condition of a black hole from where no photon can escape.
3. Derivation of Correct Gravitational Redshift
It is the basic assumption of GR that all forms of mass and energy, including mass equivalent of photon energy,
do experience gravitational interaction, just as a conventional test mass ‘m’ does. In section 2 we analyzed the
gravitational redshift by commencing from gravitational potential equation (2), which implied constant unit test
mass. Here we shall analyze gravitational redshift by commencing from gravitational force equation (1). Let us
consider the gravitational attraction experienced by a photon of frequency ν, energy E=hν and dynamic equivalent
mass hν/c2, in the gravitational field of a massive, spherically symmetric body of mass M. The gravitational force
Fg acting on a test body of mass m, located at distance r from the center of the gravitating body is given by equation
(1). Similarly, the gravitational force Fg acting on a photon of dynamic equivalent mass hν/c2 located at distance r
from the center of the gravitating body is given by,
Fg󰇛r󰇜=−GMhν
r2c2=−h
c2GMν
r2 (9)
When a photon moves against this gravitational force Fg from a location with smaller radius r to a bigger radius R,
it will lose some of its energy to the gravitational field and its frequency ν will get reduced. Hence, during the
motion of the photon from r to R, its frequency ν will not remain constant but will keep decreasing steadily, unlike
the mass m of a test body in equations (1) and (2). A small increment of energy dE, lost by the photon in moving
from r to r+dr against Fg is given by,
dE = Fg(r).dr =

dr (10)
However, since the photon energy is given by E=hν, the energy differential dE is given by,
dE = h.dν (11)
From equations (10) and (11), we get the relation,
h. =

dr (12)
Integrating equation (12) between limits r=R1 to R2 with corresponding ν=ν1 to ν2, we get,
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ν
ν2
ν1=−GM
c2dr
r2
R2
R1 (13)
That is, log𝜈2
𝜈1=𝐺𝑀
𝑐2󰇣1
𝑅21
𝑅1󰇤
Or, ν2
ν1=e
GM
c2󰇣1
R11
R2󰇤 (14)
Equation (14) gives the correct gravitational redshift relation when a photon of frequency ν1 moves out from radius
R1 of a gravitating body of mass M to a higher radius R2 where the reduced frequency is ν2. When radius R2 tends
to infinity in equation (14), the frequency ν2 of the escaping photon will be given by,
ν2
1e GM
c2R1 (15)
If a photon of frequency νe is emitted from the surface of a gravitating body of surface radius R0 and mass M, then
its escape frequency ν2 will begiven by equation (15) as,
ν2
ee GM
c2R0 (16)
Equation (16) shows that the escape frequency of any photon emitted from a gravitating body of finite mass M
and finite R0 can never vanish. If we substitute the value of Schwarzschild radius Rs from equation (8) into equation
(16) we get the escape frequency ν2 as,
ν2
ee Rs
2R0 (17)
These calculations clearly show that light photons cannot be trapped by any finite mass Black Hole. Hence it stands
proved that for a gravitating body of any finite mass M, there is no Black Hole effect and the very notion of a
Black Hole is a fantasy. The error in standard derivation of gravitational redshift as presented in equations (5), (6)
and (7) is essentially rooted in the wrong use of standard gravitational potential, derived with a test body of constant
mass m and used for the redshift analysis of a photon of variable energy in the gravitation field.
4. Inconsistencies in the Current Models of Core Collapse in CCSNe
As per current models of CCSNe, when a massive star of more than 10 solar masses, exhausts its nuclear fuel and
its thermal pressure is no more sufficient to balance the pull of gravity (Hix et al., 2014), its core starts collapsing
under gravity. However, with increasing core density, the freed electrons create sufficient degeneracy pressure to
halt further gravitational collapse. When the core mass exceeds 1.4 times the mass of the Sun, the electron
degeneracy pressure will no longer be sufficient to halt the gravitational collapse (Motch, Hameury, & Haensel,
2003), resulting in CCSNe. If the core remaining after the CCSNe is less than 2.5 times the mass of the Sun, then
the neutron degeneracy pressure will be able to balance the pull of gravity and the collapsed core will get stabilized
into a Neutron star. If the core remaining after the CCSNe is more than 2.5 times the mass of the Sun, no known
repulsive force inside a star can push back hard enough to prevent gravity from completely collapsing the core
into a black hole (Lattimer, 2012).
One significant point to be highlighted here is that the force of gravitation or the pull of gravity is always zero at
the center of any gravitating body like a star or a stellar core. It is therefore, paradoxical to model the collapse of
a stellar core to a central point where the pull of gravity is zero. However, under gravitational forces, the stellar
gases do get compressed and it is the pressure gradient which balances the pull of gravity as,
𝑑𝑃
𝑑𝑟 =−G𝑚󰇛𝑟󰇜𝜌
𝑟2=−4𝜋
3𝐺𝜌2𝑟 (18)
Here P is the hydrostatic pressure at radius r, ρ is the density and m(r) is the mass enclosed within radius r.
Assuming the pressure at the outermost radius Rm to be zero, integration of this equation yields,
𝑃=
𝐺𝜌𝑅−𝑟
Since the hydrostatic pressure in a gravitating body of mass M becomes maximum Pc at the center, its density ρ
may also vary with radius r and become maximum ρc at the center. As such we may assume a linear variation of
density with radius as,
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ρ=ρ󰇡1
󰇢 (19)
Therefore,
m󰇛r󰇜=4πrρ󰇡1
󰇢
dr=4πρ󰇣
󰇤 (20)
And M=
R (21)
With this value of m(r) and ρ equation (18) transforms into,
𝑑𝑃
𝑑𝑟 =−G𝑚󰇛𝑟󰇜𝜌
𝑟2=−4𝜋𝐺𝜌
𝑐2󰇣𝑟
3𝑟2
4𝑅𝑚𝑟2
3𝑅𝑚+𝑟3
4𝑅𝑚2󰇤 (22)
Integrating equation (22) for radius from 0 to r and pressure from Pc to P we get,
P=P
−4πGρ󰇣

+
󰇤 (23)
And Pc=5πGρc2
36 Rm2 (24)
Combining equations (21) and (24), we get the pressure Pc at the center of a gravitating body of mass M as,
Pc=5GM
12 ρc
Rm (25)
Now, let us first consider the variations of central pressure Pc and the central mass density ρ
c in spherically
symmetric gravitating bodies of up to 30 solar masses, assuming the absence of any fusion reactions. From known
values of mass and radius of certain stellar bodies, using equation (21) we get the generic value of central mass
density ρc to be of the order of 104 kg/m3. From equation (24) we get the generic value of central pressure Pc to be
of the order of 106 to 107 GPa. Equation (22) shows that the inward pull of gravity is essentially balanced by the
pressure gradient dP/dr, which in turn is mainly governed by the mass density profile from the center to the
periphery of the gravitating body. It is important to note that the inward strong pull of gravity is not balanced by
the central pressure Pc by itself; it is balanced by the pressure gradient which is zero at the center.
Equation (25) shows that with constant mass M, the central pressure Pc is directly proportional to the central mass
density ρc and inversely proportional to the maximum radius Rm. When the core temperature Tc rises with the
thermal energy input from fusion reactions, it will obviously lead to the rise in central pressure Pc. However, any
rise in central pressure Pc will be governed by equation (25) to ensure that the inward strong pull of gravity is kept
in balance. That means, the increase in Pc will lead to increase in central mass density ρc and corresponding
decrease in maximum radius Rm as per equation (21). Of course, with increase in pressure and temperature the
degree of ionization in the central core is expected to increase with consequent increase in density. On the other
hand, when the fusion reactions in the stellar core get terminated, the decrease in core temperature will obviously
lead to decrease in central pressure Pc. From equation (25), decrease in Pc will lead to decrease in central mass
density ρc and corresponding increase in maximum radius Rm as per equation (21). The decrease in ρc will be
associated with corresponding decrease in degree of ionization in the central core.
This result contradicts the core collapse predictions of current models at the end of fusion reactions. The current
models create a popular impression that a very strong force of gravitation is pulling the stellar core mass towards
its center and a very strong central pressure is required to balance the pull of gravity to prevent core collapse. As
we have seen above, the pull of gravity is zero at the center of a gravitating body and is strongest at the periphery.
This pull of gravity is balanced by the pressure gradient and not by the central pressure. Even for great variations
of central pressure and temperature, the required pressure gradient can still be maintained by self-adjustment of
mass density profile through equation of state and atomic ionization levels.
Further, the current models of core collapse are essentially based on the kinetic theory for ideal gases (Janka,
Langanke, Marek, Martinez-Pinedo, & Mueller, 2007). In the kinetic theory all constituents of the gas are assumed
to be non-interacting, except during collisions. That is, during the time interval between two successive collisions,
the momentum and kinetic energy of the gas constituents does not vary. It is only the particle momentum and
kinetic energy that account for all pressure and temperature effects. However, in stellar core high density plasma
environment all constituent particles, namely electrons, nuclei and ions, cannot be assumed to be non-interacting.
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Except when electrons are bound to the atomic nuclei in appropriate orbitals, all free electrons and corresponding
ions and nuclei will exert mutual electrostatic forces which cannot be neglected or overlooked. In situations of
high core densities, atoms and ions may be regarded as relatively fixed and vibrating about certain mean positions.
In this regard we may define the term ‘high density’ as the density of core constituents when the mean separation
distance between atoms or ions is less than the normal mean size of their parent atoms. As such, the applicability
of kinetic theory of ideal gases breaks down when core constituents assume high density.
In all current models, electron degeneracy pressure plays a crucial role in predicting the death of all massive stars.
In the treatment of electron degeneracy pressure, unbound or free electrons are supposed to acquire very high
momentum and kinetic energy through the operation of Heisenberg uncertainty principle without any electrostatic
interaction with any of the neighboring ions or electrons (Couch, 2017). This momentum creates electron
degeneracy pressure which is given by Pr = n.v.p where n is the number density, v the mean speed and p the
average momentum of the degenerate electrons. Such degenerate electrons are supposed to keep moving at near
light speeds, through the dense lattice of heavy ions in the core and get rebound from the core surface after
collisions with particles of high-pressure gases in the surrounding shell. But throughout such high-speed motion,
these degenerate electrons do not experience any electrostatic interaction with highly charged lattice ions and
hence do not lose any energy or momentum through such interactions. However, the inward gravitational pull is
mainly experienced by the heavy lattice ions with which there is no interaction of the degenerate electrons.
In dense plasma theory the Coulomb coupling parameter Γ is defined as the ratio of the mean potential energy per
particle to the mean kinetic energy per particle. It measures the degree to which many-body interactions affect the
dynamics of particles in the system. The system is said to be strongly coupled when Γ>>1 and interparticle
interactions strongly affect the beha vio r of in dividual parti cles. As such high-density stellar cores with high density
ions and free degenerate electron gas, like solid iron cores in CCSNe, must be analyzed as strongly coupled
plasmas or partially non-neutral plasma systems.
5. Analysis of Gravitation Induced Stresses in a Solid Iron Core
Let us consider a spherically symmetric solid iron body of density ρ and radius R. Let this body be in static
equilibrium under the influence of self-gravitation forces and the resulting compressive stresses in the body. For
analysis of the body stresses, we can assume the solid iron body to be an elastic continuum of bounding radius R.
At any ra diu s r wit hin this ela stic body, le t Fr be the magnitude of inward acting gravitational force per unit volume.
In addition, let us assume that a hydrostatic pressure P0 is acting on the surface r=R of this body. Due to this surface
pressure, a body force Fp proportional to dp/dr or p' will get induced in the body. Under the action of these central
force Fr and F
p the whole body will experience radial compression which can be quantified with a radial
displacement vector ur. The radial and hoop strains induced by the displacement vector ur are given by,
err =∂ur
∂r ; eθθ =ur
r ; eϕϕ =ur
r (26)
For analysis of stresses under the present spherically symmetric gravitational and hydrostatic loading, we can
neglect the Poisson’s ratio. Taking the effective modulus of elasticity as E, the equilibrium equations of elasticity
(Sandhu, 2009), with central body forces Fr and Fp can be written as,
E󰇣
+


u󰇤=−F−F=−󰇛󰇜
−p󰆒 (27)
Where M(r) is the mass of body enclosed within radius r,
M󰇛r󰇜=
πrρ (28)
From equations (27) and (28), we get the final equilibrium equation in terms of radial displacement vector ur as,
2ur
∂r2+2
r∂ur
∂r 2
r2ur=−4πGρ2
3E r−p
E (29)
Since due to spherical symmetry of the body the displacement vector vanishes at the origin, an essential boundary
condition for the solution of equilibrium equation (29) is that ur must be zero at r=0. With this boundary condition,
we obtain the solution of equation (29) as,
ur=−2πGρ2
15E r3p
4Er2 (30)
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With the displacement vector and induced strains given by equations (30) and (26), we obtain the radial and hoop
stresses as,
Radial stress σrr =E.e
rr =E.∂ur
∂r =−2πGρ2
5r2p
2r (31)
Hoop stress σθθ
ϕϕ =E.ur
r=−2πGρ2
15 r2p
4r (32)
Since the hydrostatic pressure induced radial stress at the surface r=R is -P0, the constant term p' in equations (31)
and (32) turns out to be 2P0/R. With this, equations (31) and (32) get modified to,
Radial stress σrr =−2πGρ2
5r2r
RP0 (33)
Hoop stress σθθ
ϕϕ =−2πGρ2
15 r2r
2RP0 (34)
It is important to note that both radial as well as hoop stresses are maximum at the surface, and reduce to zero at
the center, r=0, of the solid iron core. Not only the stresses, even the gravitational force Fr reduces to zero at the
center of the solid core for all possible values of density ρ. Hence, a solid iron core can never collapse under
gravitational forces contrary to the current predictions of many mathematical models.
Let us now work out the maximum radial stress σRR, in gigapascals (GPa), at the surface of the solid iron core of
earth with radius R=1220 km and density ρ=13000 kg/m3, when a constant hydrostatic pressure of P0= 330 GPa is
acting on its surface.
𝛔𝐑𝐑 =−2πGρ2
5R2−P0=−2π×6.67×10−11×130002×12202×106
5×109 330 = −351 GPa
The actual pressure in the Earth's inner core is estimated at about 360 GPa, with corresponding temperature of
about 6000 Kelvin. That means, the hydrostatic pressure of 330 GPa acting on the surface of the inner solid core
is due to the molten outer core and remaining mass of earth. Further, it can be easily seen from equation (33) that
when external hydrostatic pressure P0 is zero, maximum radial stress of about -350 GPa will be induced in a solid
iron core of about 5000 km radius. Even then the radial and hoop stresses will be zero at the center of such solid
iron core. Of course, the gravitational force is always zero at the center of any spherically symmetric gravitating
body. However, for the central iron core of about one solar mass, maximum radial stress at the outer radius can be
of the order of 106 GPa.
6. An ensemble of Iron Atoms subjected to High Pressure
Taking the radius of a normal Fe atom to be 128 picometer (pm), let us consider two iron atoms A and B, separated
by a distance d0 of 256 pm. Each Fe atom consists of a central nucleus containing 26 protons and 30 neutrons and
surrounded by 26 electrons arranged in 4 shells with electron configuration as, 1s22s22p63s23p63d64s2. Here the
electron orbits in the innermost shell are most tightly bound to the nucleus with about 7 keV binding energy per
electron, whereas the valence electron orbits in the outermost shell are most weakly bound to the nucleus with
about 8 eV binding energy per electron. Spatial orientations of all electron orbits in different shells are so aligned
as to minimize the mutual interaction energy of all orbital electrons (Sandhu, 2018). Let us assume that we can
apply equal and opposite forces Fa on the nuclei of atoms A and B so as to push the two atoms closer to, say, a
separation distance d1=200 pm. As the two atoms come closer under the action of externally applied force Fa, the
orbital electrons from the two atoms will, through electrostatic interaction, exert mutual repulsion force Fo so as
to distort or deform the original electron orbits. The mutual repulsion force Fo experienced by the orbital electrons
of both atoms will get passed on to their parent nuclei due to tight binding of the orbiting electrons. With the
deformation of original electron orbits, electronic shielding of the two nuclei will get reduced and they will also
start repelling each other with an electrostatic repulsion force of Fn. At the new separation distance d1, externally
applied force Fa will get balanced by the sum of the two repulsion forces, Fo from the deformed orbits and Fn from
the two nuclei. That is,
F
a = Fo + Fn. (35)
We may quantify the relative displacement of two atoms A and B with a term linear compression εc defined as
εc=(d0-d1)/d0. For small values of compression εc between the two atoms, major contribution to the induced
repulsion force will be Fo from orbiting electrons and the contribution from nuclear repulsion Fn will be small. As
we steadily increase εc by increasing Fa, increased value of orbital repulsion force Fo will lead to pushing out the
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loosely bound outer shell electrons to convert the parent atoms into ions. The removed electrons leave the shell
orbits of their parent atoms and come under the influence of joint electrostatic field of both ions A and B. With
this weak ionization of the original atoms under compression, the induced repulsion force Fn from the two nuclei
will increase relative to the repulsion force Fo from the deformed orbits. As we keep increasing the linear
compression εc between two atoms A and B, by increasing the externally applied force Fa, the degree of ionization
will keep increasing along with corresponding increase in induced repulsion force Fn from the two nuclei.
We may now extend this analogy of two atoms under linear compression to an ensemble of atoms in 3D space,
subjected to radial compression under externally applied high pressure force. Out of this ensemble of atoms, any
particular pair of atoms A and B, will experience linear compression εc with corresponding mutual repulsion force
as the sum of its Fo and Fn components. Depending upon the level of linear compression εc the two atoms will also
get partially ionized. In fact, what is true for atoms A and B, will be true for any pair of adjoining atoms in this
ensemble. That is, under externally applied high pressure, all pairs of atoms in the ensemble will experience
relative linear compression, relative mutual repulsion and partial ionization. The group of all electrons, freed by
the ionization process, will move under the combined electrostatic potential of all ions in the ensemble and may
be considered as degenerate electrons or Fermi electrons. However, these free electrons can never be considered
non-interacting and can never be treated as an ideal gas.
If, in addition to high pressure, the ensemble of atoms considered above, are also subjected to very high temperature
then the atomic nuclei will experience forced oscillations at high thermal or kinetic energies. At very high thermal
energies, the vibrating atoms can get fully ionized, and the internal repulsive forces in the ensemble of ions will be
mainly governed by the electrostatic nuclear repulsion forces between all pairs of ions. Therefore, the freed-up
electrons will get pushed out from the close vicinity of the vibrating ions and start moving under the combined
electrostatic field of the ensemble of ions. Even under conditions of high density and temperature, when all orbiting
electrons get stripped off from their parent atoms, current models support an untenable assumption that the freed
electrons, somehow, still remain in the vicinity of the nuclei to effectively shield the charge of ions.
This apparently free stream of electrons will quite probably start circulating on the surface of the ensemble of ions
as a degenerate electron gas, thereby giving rise to high magnetic fields in the body of ion ensemble. Whatever
number of high-speed free electrons happen to streak across the ion ensemble, will steadily lose energy through
electromagnetic interactions and get captured in some or the other ion. Such captured electron may get re-emitted
under the influence of high temperature thermal vibrations of the ions, to rejoin the stream of free electrons on the
surface of the ensemble. This process of free electrons streaking across the ion ensemble, radiating energy during
their capture and again getting re-emitted to rejoin the surface free electrons, may in fact provide an effective
cooling mechanism for the hot ensemble of ions. However, there is an exception in metallic bonds when atoms
share their valence electrons and free electrons keep moving at slow speeds through interstitial spaces in crystal
lattice, without getting captured or re-emitted.
7. Electrostatic Pressure Generated in Iron Core Under Extreme Compression
Let us consider a typical iron stellar core under high-pressure, as an ensemble of ions discussed in previous section.
Depending on the temperature and pressure profile in the core body, the degree of ionization may vary across the
core. When the fusion reactions stop and the core gets cooled, the degree of ionization may reduce to a minimum
at the center and maximum at the surface due to external pressure. However, we may assume a uniform degree of
ionization q throughout a thin spherical shell within the core body. That is, we assume the positive charge on all
iron ions in the thin spherical shell to be +qe where q may be of any value between 0 and 26 and e is the magnitude
of the electron charge. Let r0 be the original effective radius of a neutral iron atom and let ri be the effective radius
of the atom or ion under compression. Then the relative linear compression, in percentage terms, will be given as,
εi=r0−ri
r0×100 (36)
With increase in linear compression εi effective ionic radius ri will keep decreasing. With decreasing ionic radius
ri, the outermost 4s valence electrons will be the first to get stripped off from the iron atom to give ionic charge
value of q=2. As we keep increasing the linear compression with corresponding decrease in ionic radius ri electrons
from the third shell with outermost orbits will keep getting stripped off and the ionic charge q will keep increasing.
As a rough estimate, typical values of r i with corresponding ionic charge q are listed in table 1. Under close packing
conditions in the ionic ensemble, we assume the atomic packing factor (APF) to be 0.74 which is a maximum for
any close packed lattice. Therefore, the nuclei density Nn as a function of ri is given by,
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24
Nn=3×0.74
4πri3 (37)
And the corresponding mass density ρi is given by multiplying Nn with mass of iron nucleus 9.27e-26 as,
ρi=N
n×9.27×10−26 (38)
Let ke be the electrostatic force constant given by (1/(4πε0))=8.98755×109. Then the electrostatic force between
two adjoining ions, separated by 2ri distance, will be given by,
Fi=keq2e2
󰇛2ri󰇜2 (39)
The electrostatic pressure between adjacent ions will be given by the electrostatic Fi divided by unit cell side area
=(1/Nn)2/3 as,
Pi=keq2e2
󰇛2ri󰇜2󰇛Nn󰇜2/3 (40)
A stellar iron core of mass greater than a solar mass will experience extreme compression at its periphery due to
gravitation induced stresses given by equations (33) and (34). While all stresses at the center of the core are
expected to be zero, the peripheral stresses are expected to be of the order of 106 to 107 GPa. Therefore, as indicated
in table 1, linear compression of iron atoms in the peripheral regions is expected to go up to 80 percent with
corresponding ionic pressure of 107 GPa. At this extreme compression, degree of ionization will reach q=16 that
corresponds to the complete stripping off of 3rd and 4th shell electrons from iron atoms. However, the stress-free
central zone of the iron core is expected to contain normal iron atoms.
Table 1. Typical Ionic parameter variations during extreme compression of Iron Core
Sl. No. Ionic radius
ri (pm)
Linear Compression
εi %
Ionic Charge
+q
Nuclei Density
N
n
per m3
Mass Density
ρi kg/m3
Ionic Pressure
Pi GPa
1. 128.0 0.0 0 8.4e+28 7.8e+3 0.0
2. 108.0 15.6 2 1.4e+29 1.3e+4 5.3e+2
3. 100.0 21.9 3 1.8e+29 1.6e+4 1.6e+3
4. 90.0 29.7 5 2.4e+29 2.2e+4 6.9e+3
5. 75.0 41.4 8 4.2e+29 3.9e+4 3.7e+4
6. 60.0 53.1 11 8.2e+29 7.6e+4 1.7e+5
7. 50.0 60.9 14 1.4e+30 1.3e+5 5.7e+5
8. 25.0 80.5 16 1.1e+31 1.0e+6 1.2e+7
9. 15.0 88.3 19 5.2e+31 4.9e+6 1.3e+8
10. 10.0 92.2 22 1.8e+32 1.6e+7 8.8e+8
11. 6.0 95.3 24 8.2e+32 7.6e+7 8.1e+9
12. 3.0 97.7 26 6.5e+33 6.1e+8 1.5e+11
13. 1.0 99.2 26 1.8e+35 1.6e+10 1.2e+13
14. 0.5 99.6 26 1.4e+36 1.3e+11 2.0e+14
In a close packed iron ion crystal lattice, with ionic mass mi, mean ionic separation 2ri, let us assume that the ions
experience thermal vibrations about their mean positions. Let their mean amplitude of oscillations be A, which is
less than ionic radius ri. The minimum ionic separation during such oscillations will be 2(ri – A) from one side ion
and corresponding maximum separation from opposite side ion will be 2(ri + A). If the ionic charge is q, the
maximum potential energy of the central ion at the instant of its maximum oscillation amplitude A will be,
EP=1
2󰇡e2
4πε0󰇢󰇣 q2
2󰇛ri−A󰇜+q2
2󰇛ri+A󰇜󰇤=keq2e2ri
2ri2−A2 (41)
However, mean potential energy of the central ion at the instant of its mean separation from both sides will be,
E0=e2
4πε0q2
2ri=keq2e2
2ri (42)
Therefore, the mean kinetic energy of the oscillating ion will be,
EK=keq2e2ri
2ri2−A2keq2e2
2ri=keq2e2A2
2ri2−A2ri=1
2miv2= 1
2kB𝑇𝑖 (43)
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At any given ionic radius r
i
with corresponding degree of ionization q, the thermal temperature T
i
will govern the
maximum ionic amplitude A. If ω is the angular frequency of oscillations with amplitude A, the maximum velocity
will be given by,
v2=k
e
q
2
e
2
A
2
m
i
r
i2
−A
2
r
i
=A
2ω2 (44)
From this relation we get the angular frequency of ionic oscillations as,
𝜔=
󰇛

󰇜
(45)
8. Invalidity of Stellar Core Collapse Models
We need to explore the basis of stellar core collapse in current models in order to examine the validity of projected
scenarios that give rise to neutron stars, and black holes.
Figure 1. Concentric shells of hydrogen, helium, carbon, oxygen and silicon fusion zones around
the central solid iron core, towards the end of hydrostatic burning in massive stars
At the end of hydrostatic burning, a massive star consists of concentric shells of hydrogen, helium, carbon, oxygen
and silicon that are the relics of its previous burning phases. Since fusion of iron produces no net energy output,
inert iron core at the center is the final stage of nuclear fusion in hydrostatic burning (figure 1). It is believed that
the iron core begins to contract by gravity when the fusion energy created thermal pressure vanishes at the end of
fusion reactions. When the iron core, formed in the center of the massive star, grows by silicon shell burning to a
mass around the Chandrasekhar mass limit of about 1.44 solar masses, it is believed that electron degeneracy
pressure can no longer stabilize the core and it collapses. This is believed to start what is called a core-collapse
supernova.
However, there is an ambiguity whether the core collapses due to the self-gravitation forces acting on the body of
iron core or whether the core collapse is caused by the unbearable outer-shell hydrostatic pressure at the end of
Silicon fusion reaction. Let us examine the validity of different claims.
A. Pull of Gravity is balanced by pressure gradient dP/dr and not by peak pressure P
c
. The Core Collapse
models create a general impression that a very strong force of gravitation is pulling the core mass towards
its center and a very strong central pressure is required to balance the pull of gravity to prevent the core
collapse. As we have seen above, the pull of gravity is zero at the center of a gravitating body and is strongest
at the periphery. This pull of gravity is balanced by the pressure gradient, which is zero at the center, and
not by the central pressure. The gravitational force per unit stellar volume is mainly governed by the mass
density profile from the center to the periphery of the gravitating body. Even for great variations of central
pressure and temperature, the required pressure gradient is maintained by self-adjustment of mass density
profile and the outer radius of the star in accordance with equation (25). Therefore, when the central
temperature and pressure reduces at the end of fusion reactions, central mass density along with degree of
ionization will decrease in the central zone and outermost radius of the stellar body will increase. With this
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the pressure gradient will match the changed mass density profile to balance the pull of gravity. Hence, there
is no question of core collapse.
B. Core cannot collapse by diminishing of fusion thermal pressure. Since the inert iron core, formed in the
center of the massive star, grows by silicon shell burning, the final stage fusion reactions were obviously
taking place at the surface of the iron core and in the inner layers of the silicon shell. If this thin fusion
reaction zone was under high thermal pressure then the same high pressure must be acting at the surface of
the iron core as well as the inner layers of the silicon shell. When the fusion reaction stops and the associated
high thermal pressure diminishes, this will obviously lead to diminishing of pressure over the surface of the
iron core. This diminished pressure over the surface of iron core may actually lead to a reduced pressure in
the silicon shell with corresponding readjustment of mass density profile in the star. As such the solid iron
core cannot collapse with diminishing of fusion thermal pressure in the silicon shell.
C. The central solid iron core cannot collapse under self-gravitation. As already seen in analysis of
gravitation induced stresses in a solid iron core, the force of gravitation, radial and hoop stresses and
hydrostatic pressure are all zero at the center of the core. While the self-gravitation induced radial and hoop
stresses keep increasing with the square of radius r2, the hydrostatic pressure is directly proportional to the
radius r. As such the gravitation and hydrostatic pressure induced stresses in the central solid iron core will
be maximum at the surface of the core and zero at the center. Therefore, the iron core cannot collapse towards
its center under any circumstances. Under current models of core collapse, the iron core pressure is analyzed
under kinetic theory of gases which is not applicable to solid bodies under extreme pressure. Further, in
order to apply the provisions of the kinetic theory of gases, free electrons, positive ions and nuclei are all
treated as non-interacting inert particles which is not valid. Whereas under hydrostatic equilibrium the
pressure becomes maximum at the center, the situation gets reversed in a solid body where the development
of hoop stresses renders the central zone stress free. Hence the central solid iron core cannot collapse towards
its center under self-gravitation.
D. Undue reliance on electron degeneracy pressure to support gravitational loading on iron core. As seen in
the previous section, when an ensemble of iron atoms is subjected to extreme compression the bound
electrons from the outer orbital shells get stripped out to a free degenerate state. These degenerate electrons
are now constrained to move under the combined electrostatic potential of the whole ensemble of iron ions
and are generally regarded as gas of free electrons moving at near light-speeds. However, one important
point which is often overlooked in current models of CCSNe is that when these degenerate electrons get
free, an equal number of positive ionic charges get accumulated on the ensemble of iron ions in the core
body. These ionic charges experience mutual electrostatic repulsive forces, thus producing internal reaction
pressure just sufficient to balance the externally applied gravitational pressure. In an isolated enclosure or
container, the degenerate electron gas will definitely exert a so called ‘degeneracy pressure’. But this
electron degeneracy pressure cannot be relied upon in the environment of stellar iron core for two reasons.
Firstly, to produce the supporting internal pressure, these high-speed electrons will have to exchange their
momentum, through elastic collisions with silicon shell nuclei, ions and atoms, which is not possible for
these electrons due to electrostatic interactions. Secondly, to produce the supporting internal pressure, these
high-speed electrons will have to traverse through the body of iron core without losing any momentum or
kinetic energy, which again is not possible due to electrostatic interactions. Therefore, it is wrong in the
current models of CCSNe to first assume the electrons, ions and nuclei to be non-interacting fermions and
then rely on their degeneracy pressures to support gravitational loading on iron core.
E. Core Collapse models propounded to Create Neutron Stars and Black Holes. Under current models of
core collapse, depending on the stellar core mass, Neutron Stars happen to be the gateways to Black Holes.
In a neutron star, the pull of gravity is supposed to be balanced or supported by neutron degeneracy pressure
up to certain mass limit beyond which it collapses into a black hole. Here too, neutrons are treated as non-
interacting inert balls whose momentum and kinetic energy contributes to the degeneracy pressure. However,
following facts easily invalidate such models of neutron stars (Sandhu, 2009).
(a) Free neutrons are unstable with half-life of about 15 minutes.
(b) Neutrons become stable only when joined to a proton through nuclear fusion.
(c) Practically no two or more neutrons can ever be joined together into a stable nuclide.
(d) Even for a super-heavy nuclide, number of neutrons cannot be more than twice the protons.
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F. Core Collapse not necessary for onset of Super Nova explosions. Well, once we find that the collapse of
central solid iron cores under any form of gravitational loading is not feasible, then an obvious question
arises regarding the cause of Super Nova explosions. This question may have to be examined in depth by
experts in the field. But prima facie it appears that while iron nuclei are being produced through silicon
fusion reactions with release of energy, a small fraction of higher mass nuclei, including fissionable nuclei,
may also get p ro du ced w ith absorption of a part of the released energy. As the central iron core keeps getting
built up steadily, the nuclei with higher atomic number, thus higher ionic charge, may keep getting diffused
to the outer surface of the core. By the time the solid iron core gains about a solar mass or so, the
concentration of fissionable nuclei on the surface of the iron core may become critical to trigger a fission
reaction, a Super Nova explosion.
9. Conclusion
In GR a mathematical abstract notion of 4D spacetime continuum has been projected as a physical entity which
could get rippled, deformed and curved. It has however been analytically proved (Sandhu, 2011) that spacetime is
not a physical entity. Due to this conceptual error in GR, various mathematical possibilities indicated by the
spacetime model are routinely being projected as physical possibilities. For example, a mathematical singularity
predicted by Schwarzschild metric solution of Einstein’s Field Equations (EFE) have been projected as a physical
possibility in Black Holes, where spacetime could be deformed and curved to an extreme to make a physical
singularity. Further, to provide an additional physical support to a mathematical notion of Black Holes, a wrong
derivation of gravitational redshift had been readily accepted as a standard. The physical basis of Black Hole
creation was further strengthened by interpreting the observations of Super Nova explosions in the framework of
core collapse models. Ultimately the core collapse models came to be regarded as the physical foundation of Black
Holes and Neutron stars. In this paper we have shown that the correct derivation of gravitational redshift does
not permit photon capture in a gravitating body of any mass or size. The invalidity of core collapse models has
been established on following grounds:
(a) Since the force of gravitation is always zero at the center of any gravitating body like a star, the stellar core
cannot collapse towards its center. The inward strong pull of gravity is not balanced by the central pressure
but by the pressure gradient which is zero at the center.
(b) Any rise in central pressure Pc will lead to increase in central mass density ρc and corresponding decrease in
maximum radius Rm. The termination of fusion reactions in the stellar core will lead to the decrease in core
temperature and pressure which will lead to decrease in central mass density ρc and corresponding increase
in maximum radius Rm. The decrease in ρc will be associated with corresponding decrease in degree of
ionization in the central core and not to its collapse.
(c) The current models of core collapse are essentially based on the kinetic theory where all constituents of the
gas are assumed to be non-interacting, except during collisions. However, in stellar core high density plasma
environment all constituent particles, namely electrons, nuclei and ions, cannot be assumed to be non-
interacting. As such, the applicability of kinetic theory of ideal gases breaks down when core constituents
assume high density.
(d) Since the degenerate electrons cannot be assumed to be non-interacting, it is not valid to assume that electron
degeneracy pressure supports the inward gravitational pull of gravity in the solid iron core.
(e) A solid iron core under spherically symmetric compression develop radial and hoop compression stresses
which are zero at the center and maximum at the periphery of the core. As such, for solid iron core
hydrostatic equilibrium equations are not applicable and its gravitational collapse impossible.
(f) Under extreme compression, orbiting electrons from outer shells of iron atoms get stripped off to constitute
Fermi gas of free electrons. The resulting positively charged iron ions develop electrostatic repulsive
pressure just sufficient to balance the gravitational loading.
(g) Formation of Neutron Stars is not possible since free neutrons are unstable and practically two or more
neutrons cannot be joined together by fusion reactions. Neutrons can become stable only when joined to a
proton by fusion reaction.
Thus, current models of stellar core collapse, that lead to the formation of Neutron Stars and Black Holes, are
erroneous, faulty and invalid. Hence Black Holes are a mathematical fantasy and not a physical reality.
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... In this paper, some of the founding assumptions of old well-established models of Astrophysics are critically examined and shown to be invalid. One such assumption is the well-known notion of electron degeneracy pressure and the second one is the extension of hydrodynamic equation of state to check the stability of non-burning high pressure, high density solid stellar cores under self-gravitation [2] [3]. ...
... The peripheral stresses are expected to be of the order of 10 7 GPa. Under this extreme compression corresponding degree of ionization will lead to complete stripping off of 3 rd and 4 th shell electrons from iron atoms [3]. ...
... In the grid locked lattice structure of gravitation induced solid state, ionized particles also undergo thermal vibrations about their mean positions. If mean amplitude of ionic oscillations is A then as per Equation (43) of [3], temperature T i and frequency ν i corresponding to such ionic thermal vibrations will be given by, ...
Article
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A well-known but erroneous notion of electron degeneracy pressure has misled Astrophysics for nearly a century now. Because of their electrostatic interactions, the electrons can never exchange their momentum with positive ions through elastic collisions and hence can never provide the so-called electron degeneracy pressure in stellar cores to counter the effect of gravity. In situations of high core densities, when the mean separation distance between atoms or ions becomes less than the normal size of their parent atoms, their electrostatic repulsion will force them into a lattice gridlock, leading to a solid state. All degenerate stellar cores constitute a solid state and the radial and hoop stresses induced by self-gravitation are proportional to the square of radius (r^2). As the size of a solid iron stellar core grows, its peripheral region will experience extreme compression and will get partially ionized due to the phenomenon of pressure ionization. All so-called Neutron Stars and Black Holes are in fact Ionized Solid Iron Stellar Bodies (ISISB). The presence of ions in the peripheral regions of the ISISB will be associated with the circulation of degenerate electrons around the surface, thereby producing strong magnetic fields. A positive excess of ionic charge in all ISISB becomes a source of Ionic Gravitation through the process of polarization of neutral atoms and molecules in stellar bodies. These ISISB are the primary constituents of AGN and are the source of all non-stellar radiation and Jets of ionized matter.
... In this paper some of the founding assumptions of old well-established models of Astrophysics are critically examined and shown to be invalid. One such assumption is the well-known notion of electron degeneracy pressure and the second one is the extension of hydrodynamic equation of state to check the stability of non-burning high pressure, high density solid stellar cores under self-gravitation [2,3]. ...
... The peripheral stresses are expected to be of the order of 10 7 GPa. Under this extreme compression corresponding degree of ionization will lead to complete stripping off of 3 rd and 4 th shell electrons from iron atoms [3]. ...
... In the grid locked lattice structure of gravitation induced solid state, ionized particles also undergo thermal vibrations about their mean positions. If mean amplitude of ionic oscillations is A then as per equation (43) of [3], temperature Ti and frequency νi corresponding to such ionic thermal vibrations will be given by, ...
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A well-known but erroneous notion of electron degeneracy pressure has misled Astrophysics for nearly a century now. Because of their electrostatic interactions, the electrons can never exchange their momentum with positive ions through elastic collisions and hence can never provide the so-called electron degeneracy pressure in stellar cores to counter the effect of gravity. In situations of high core densities, when the mean separation distance between atoms or ions becomes less than the normal size of their parent atoms, their electrostatic repulsion will force them into a lattice gridlock, leading to a solid state. All degenerate stellar cores constitute a solid state and the radial and hoop stresses induced by self-gravitation are proportional to the square of radius (r 2). As the size of a solid iron stellar core grows, its peripheral region will experience extreme compression and will get partially ionized due to the phenomenon of pressure ionization. All so-called Neutron Stars and Black Holes are in fact Ionized Solid Iron Stellar Bodies (ISISB). The presence of ions in the peripheral regions of the ISISB will be associated with the circulation of degenerate electrons around the surface, thereby producing strong magnetic fields. A positive excess of ionic charge in all ISISB becomes a source of Ionic Gravitation through the process of polarization of neutral atoms and molecules in stellar bodies. These ISISB are the primary constituents of AGN and are the source of all non-stellar radiation and Jets of ionized matter.
... In a recent paper [4] it has already been shown that Black Holes are a mathematical fantasy and not a physical reality. Specifically, it has highlighted the impossibility of photon capture in any gravitating stellar body. ...
... When the hydrostatic equilibrium is achieved, the acceleration term in equation (4) will vanish and the equilibrium equation for pressure P will be given as, = −G ( ) 2 (5) In general, any change in hydrostatic equilibrium will lead to mass transfers between different radial shells that will be governed by equation (4). The density and pressure profiles will get readjusted before a new equilibrium is achieved. ...
... Let us consider an ensemble of atoms in a spherically symmetric solid iron core, subjected to extreme radial compression. Depending upon the level of compression the orbiting electrons of adjoining atoms will get pushed out resulting in partial or full ionization [4]. This phenomenon is also known as 'pressure ionisation'. ...
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The notion of electron degeneracy pressure in stellar core collapse models is founded on the assumed non-interacting characteristic of electrons and ions. As non-interacting particles, electrons and ions are assumed to be identical to the ideal gas particles in kinetic theory, which produce kinetic pressure through exchange of momentum in elastic collisions. Actually, electrons cannot exchange momentum with positive ions due to their electrostatic interaction and hence cannot provide the much-acclaimed degeneracy pressure. This non-interacting characteristic of electrons and ions is also assumed to invoke the use of hydrostatic equilibrium equations for analysing the stability of high-density solid stellar cores. By taking into account the electromagnetic interactions among electrons and ions we show that the high-density stellar cores transform into gravity induced solid state, which can support the gravitational loading through development of radial and hoop stresses. In solid state the induced stresses can only be analysed by equilibrium equations of elasticity. Their solution for a spherical solid body yields the radial and hoop stresses proportional to square of radius. Hence, the self-gravitation induced stresses are maximum at the periphery and zero at the centre, which makes it impossible for a massive stellar core to collapse under self-gravitation into fictitious Black Holes. We conclude that all stellar cores which are said to be degenerate, where some sort of degeneracy pressure is invoked to prevent their gravitational collapse under hydrostatic equilibrium conditions, are in fact solid stellar cores which acquire their stability under self-gravitation through equilibrium equations of elasticity.
... In a recent paper [3] it has already been shown that Black Holes are a mathematical fantasy and not a physical reality. Specifically, it has highlighted the impossibility of photon capture in any gravitating stellar body. ...
... Let us consider an ensemble of atoms in a spherically symmetric solid iron core, subjected to extreme radial compression. Depending upon the level of compression the orbiting electrons of adjoining atoms will get pushed out resulting in partial or full ionization [3]. This phenomenon is also known as 'pressure ionisation'. ...
... A vast majority of more than 90% of all stars, including our sun, are expected to finally evolve into White Dwarfs. As far as Black Holes are concerned, we have already seen that in the absence of stellar core collapse phenomenon, Black Holes are a mathematical fantasy and not a physical reality [3]. Therefore, less than 10% of all stars finally end up in the so-called Neutron Stars, mostly through the process of Super Novae explosions. ...
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Theoretical models of the equation of state (EOS) of neutron-star matter (starting with the crust and ending at the densest region of the stellar core) are reviewed. Apart from a broad set of baryonic EOSs, strange quark matter, and even more exotic (abnormal and Q-matter) EOSs are considered. Results of calculations of M_max for non-rotating neutron stars and exotic compact stars are reviewed, with particular emphasis on the dependence on the dense-matter EOS. Rapid rotation increases M_max, and this effect is studied for both neutron stars and exotic stars. Theoretical results are then confronted with measurements of masses of neutron stars in binaries, and the consequences of such a confrontation and their possible impact on the theory of dense matter are discussed.
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