Gravitational collapse is logically impossible

In kinetic theory of ideal gases, the kinetic pressure is generated through momentum exchange of identical non-interacting particle in elastic collisions. Similarly, the electron degeneracy pressure is assumed to be generated through momentum exchange of free non-interacting electron particles in elastic collisions. At high core densities, when a star begins to cool down, electron degeneracy pressure is assumed to be the only mechanism available to support the inward pull of gravity. In the absence of adequate thermal pressure, gravity will accelerate heavy ions radially inwards and to counter this inward acceleration, the high-speed electrons will be required to push these ions radially upwards, by their degeneracy pressure, that is by exchanging their momentum through elastic collisions with these ions.

Actually however, due to their electrostatic interactions high energy free electrons cannot exchange their momentum with positive ions, through elastic collisions. That means the electron degeneracy pressure can be produced only if we assume the electrons, protons, and positive ions to be non-interacting. Since the 'electron degeneracy pressure' is the crucial fundamental concept in all Stellar Core Collapse Models, that lead to the formation of Black Holes, it implies that the electrons, protons, and positive ions are always assumed to be non-interacting in such models. Hence, the popular notion of electron degeneracy pressure is founded on the faulty assumption of non-interacting electrons and protons and there is no physical mechanism to support this notion.

Unfortunately, the current models never examine the possibility of mutually interacting ensemble of core constituents transforming into a solid state at high densities and developing shear, radial and hoop stresses to support the pull of gravity. As in various arches and dome structures, development of compressive hoop stresses in spherical shells, is the best physical mechanism of supporting the solid stellar cores against gravitational loading.

In hydrostatic equilibrium of a stellar body, all constituent particles are assumed to freely move past one another. However, in situations of very high core densities, atoms and ions will occupy relatively fixed positions and may experience thermal vibrations about their mean positions. When the mean separation distance between ions is less than the normal mean size of their parent atoms, of the order of Bohr radius or less, the electrostatic repulsion between the ions will force them into a lattice gridlock, leading to a solid state. In a solid state, particles maintain their normal separations through mutual interactions and cannot move past one another. It must however, be kept in mind that this is not a ‘naturally’ or freely occurring solid state but a ‘forced’ solid state brought about under extreme gravitational loading in a stellar core.

Thus, mutually interacting ensemble of positive ions in stellar cores, transforms into a solid state under self-gravitation and develop shear, radial and hoop stresses to support the pull of gravity. Development of compressive hoop stresses in spherical shells, is the best physical mechanism of supporting the solid stellar cores against gravitational loading. Central regions of all high-density stellar cores will physically constitute a solid state. Stresses induced in such cores due to self-gravitation can only be analysed through equilibrium equations of elasticity and not by hydrostatic equilibrium equations of the kinetic theory. The solution of equilibrium equations of elasticity for a spherically symmetric solid sphere yield the radial and hoop stresses induced by self-gravitation to be proportional to the square of radius (r2). The most remarkable feature of the self-gravitation induced radial and hoop compressive stresses is that they are maximum at the periphery and zero at the centre of the solid stellar core. This makes it impossible for the stellar core to collapse under self-gravitation. In contrast, by assuming the contents of a self-gravitating stellar core to be non-interacting, we transform the actual solid state to hypothetical fluid state where the hydrostatic pressure is always maximum at the centre. Hence it is concluded that the current models of Stellar Core Collapse, founded on the invalid assumption of non-interacting core constituents, has mislead Astrophysics into the realm of fictitious Black Holes.

Article Demystification of the spacetime model of relativity

Article Black Holes are a Mathematical Fantasy, not a Physical Reality

Article Stellar Core Collapse Models are Erroneous and Misleading

Article Ionic Gravitation and Ionized Solid Iron Stellar Bodies

Article Cosmological Redshift Caused by Head-On Collisions with CMB ...

At first glance, it seems quite natural that the counteraction to the collapse of stars is the compression of their physical bodies to certain limits of matter density. It is believed that for each object (stars, planets...) there is a density limit, overcoming which will inevitably lead to the collapse of the object. But this non-relativistic approach is applicable only in Newton's theory of gravitation, where time is a parameter of various processes occurring in a flat three-dimensional (Euclidean) space. The mathematical basis of GTR is a four-dimensional curved (pseudo-Riemannian) space — space-time. In the minds of people, Time and Space belong to different categories of perception: they are even measured by different instruments - clocks and rulers. Since the space-time of GTR has a 4-dimensional curvature, it is obvious that the readings of the "clock" and "rulers" at each of its points must depend on the values ​​of the time and space coordinates of this point.

The problem of measurements in GTR hd been solved in 1944 by Zelmanov in his theory of physical observable quantities — chronometric invariants (for detil, see the survey [1]). The reference frame of a physical observer is determined by a 4-dimensional real velocity vector. Physical observable characteristics are: time, 3-dimensional space, gravitational-inertial force, tensors of angular velocity of rotation and deformation rates of the observed 3-space. The interval of observable time depends on the value of the gravitational potential of the frame of reference, as well as on the scalar product of the three-dimensional velocities of rotation and translational motion of the three-dimensional observable space. Formally, time for a physical observer can go: 1) from the past to the future (forward motion); 2) from the future to the past (reverse motion); 3) stop. The collapse condition is directly related to the stop of observable time, which is easy to see in the example of the well-known Schwarzschild metric in the empty space-time of GTR. The empty three-dimensional observable Schwarzschild space does not rotate or deform, but collapses under the condition that the time component of the metric tensor is 0, i.e., the observed time stops. This condition is satisfied on the surface of a sphere whose radius is equal to the gravitational radius of the body. For the Earth, the gravitational radius is 0.887 cm, for the Sun it is 2.93 km. They are determined by the values ​​of the masses and radii of the bodies in question. On the surface of the source of the gravitational field, time stops for the observer, but there is no talk of the density of the body, which supposedly prevents the collapse process. Collapse is not the compression of the body to a monstrous density, but simply a state in which proper time stops for the observer. But it is this surface on which the observed time stops that is the center of gravitational attraction of bodies.

Calculations show that in a non-rotating frame of reference, in particular, in Schwarzschild space-time, time for a physical observer stops on a spherical surface, the radius of which is equal to the gravitational radius of the body. The gravitational potential of the body on this surface is equal to the total (maximum) energy of the body E = mc^2. The derivative of the potential with respect to the radial coordinate, related to the mass of the body, is the acceleration of gravity, i.e. Galileo's principle is fulfilled [2]. Thus, it is the surface of the gravitational collapsar inside our planet that attracts all bodies located in the gravitational field of the Earth. Here it is appropriate to give the following example. The trunks of trees growing on the slopes of mountains, ravines... are always directed not perpendicular to the slope, but are oriented exactly to the center of the Earth. In exactly the same way, a person perceives with his consciousness the concepts of "up" and "down", namely, as directions to the centre of the Earth and from its centre. Therefore, people located at different latitudes, from the poles to the equator, always see the sky above their heads and the surface of the Earth under their feet.

1. Rabounski D. and Borissova L. Physical observables in General Relativity and the Zelmanov chronometric invariants. Progress in Physics, 2023, no.1, 3-29.

2. Borissova L. and Rabounski D. Galileo Principle and the origin of gravitation according to Generai Relativity. Progress in Physics, 2024, no.2, 69-78.