The Black Hole – Can the ‘Irresistible Force’ Overcome the ‘Immovable Object?’

Written by Raymond HV Gallucci, PhD, PE on March 26, 2018. Posted in Current News

The past decade of work by Stephen Crothers (pictured), following some earlier work by Antoci and Abrams, has focused on mathematically demonstrating the impossibility of the black hole, consistent with the original analysis by Karl Scwarzschild.

This paper briefly reviews Crothers’ work, then presents a physical argument against the credulity of the black hole.  This argument examines the extreme difficulty, if not altogether impossibility, of the ‘irresistible force’ of increasing gravity allegedly collapsing a neutron star into an even greater ‘immovable object’ of increasing density – a black hole.

The Black Hole – Can the ‘Irresistible Force’ Overcome the ‘Immovable Object?’

 Raymond HV Gallucci, PhD, PE, 8956 Amelung St., Frederick, Maryland, 21704

e-mails: [email protected], [email protected]

Following some earlier work by Antoci and Abrams, Crothers has spent at least the past decade arguing the mathematical impossibility of the black hole.  Following a brief review of the mathematical argument, a physical one is presented, based on analysis of the ‘irresistible force’ of increasing gravity allegedly collapsing a neutron star with an even greater ‘immovable object’ of increasing density into a black hole.  This physical argument supports Crothers’, et al., contention that a black hole is both a mathematical as well as physical impossibility.

1. Introduction

which becomes indeterminate at the ‘Schwarzschild radius.’

2. The Black Hole – Is it Even Physically Plausible?

The preceding is a mathematical description of the (erroneous) basis for the existence of a black hole.  What about a physical interpretation?  Is it conceivable that a star could gravitationally collapse indefinitely, i.e., beyond even the density of neutronium (approximately 4 x 10¹⁷ kg/m³), into a singularity?  Let us begin with a neutron star, at least three times the mass of the sun (https://en.wikipedia.org/wiki/Neutron_star), with a scaled radius of 1.  At its surface, the gravity, scaled to a gravitational constant and stellar mass of unity, is 1.  As the star collapses upon itself, its radius decreases, corresponding to an increase in density (but not mass) and an increase in surface gravity with the inverse square dependence of gravity on radius.  Decreasing the star’s radius by 25{154653b9ea5f83bbbf00f55de12e21cba2da5b4b158a426ee0e27ae0c1b44117} each time (i.e., the radius reduces to  with each decrease ‘n’), it takes only eight such decreases to reduce the radius to 0.1, an additional eight to drop to 0.01, and another eight to 0.001.  Surface gravity, proportional to the inverse square of the radius, increases one-thousand fold after n = 24, while the star’s density, proportional to the inverse cube of the radius, increases one-million-fold.  In fact, with each decrease, the density-to-surface gravity ratio increases by a factor of  until, after n = 24 decreases, it is 1000.  Given this ratio, does it make sense that the ‘irresistible force’ of increasing gravity should continue to overcome the ‘immovable object’ of even greater increasing density until this density is one-million times that of neutronium?  Or would the collapse arrest at some point where the density cannot be increased and either an unimaginable ‘implosion’ occurs, releasing up to the energy equivalent of the star’s mass, or the densest possible neutron star exists (but not a black hole)?

Meanwhile, as the star’s radius decreases, what is the net gravity at various locations within the star itself?  Inside a solid sphere of uniform density at radius r, gravitational force rises linearly from zero at the center of the solid sphere to its maximum value at the sphere’s surface. (Wilhelm, F., “Gravitational Force on a Point-Mass M inside a Solid Sphere or Solid Shell, with Uniform Mass Distribution,” 2005, http://www.heisingart.com/dvc/ch{154653b9ea5f83bbbf00f55de12e21cba2da5b4b158a426ee0e27ae0c1b44117}2013{154653b9ea5f83bbbf00f55de12e21cba2da5b4b158a426ee0e27ae0c1b44117}20Gravitational{154653b9ea5f83bbbf00f55de12e21cba2da5b4b158a426ee0e27ae0c1b44117}20force{154653b9ea5f83bbbf00f55de12e21cba2da5b4b158a426ee0e27ae0c1b44117}20on{154653b9ea5f83bbbf00f55de12e21cba2da5b4b158a426ee0e27ae0c1b44117}20a{154653b9ea5f83bbbf00f55de12e21cba2da5b4b158a426ee0e27ae0c1b44117}20point{154653b9ea5f83bbbf00f55de12e21cba2da5b4b158a426ee0e27ae0c1b44117}20inside{154653b9ea5f83bbbf00f55de12e21cba2da5b4b158a426ee0e27ae0c1b44117}20a{154653b9ea5f83bbbf00f55de12e21cba2da5b4b158a426ee0e27ae0c1b44117}20spherical{154653b9ea5f83bbbf00f55de12e21cba2da5b4b158a426ee0e27ae0c1b44117}20shell.pdf)  This follows readily from gravity arising only from the portion of the sphere < r, for which the enclosed mass is proportional to the cube of the radius, while the gravitational force at r is proportional to the inverse square of the radius.  Combined, these yield a linear dependence of gravity with r.

Figure 1 displays the following: (1) the scaled surface gravity, scaled stellar density and density-to-surface gravity ratio as the stellar radius decreases from 1 to 0.001 (dotted, dashed and solid lines, respectively) and (2) the scaled gravity at various radial positions (shown as individual points), inside, on the surface, and outside the star as it collapses (e.g., radial position  is inside the star for smaller stellar radii [shown down to 0.001], on the surface at that stellar radius, and outside the star for larger stellar radii [up to 1]).  Clearly evident is the one-billion-fold increase in stellar density, one-million fold increase in surface gravity, and one-thousand fold increase in their ratio when the stellar radius decreases one-thousand fold.  Also evident at each radial position is the increase in gravity while that position lies within the star, with it reaching its maximum, constant value once the stellar radius reaches that position.  Since this never exceeds the maximum gravity at the stellar surface, the density-to-gravity ratio must always be greater than or equal to that at the stellar radius.  This further suggests the dominance of the ‘immovable object’ aspect of the increasing density over the ‘irresistible force’ aspect of the increasing gravity, lending a physical basis to the mathematical one for the impossibility of a black hole.

3. Conclusion

FIGURE 1.  Increases in Scaled Values with Decreasing Stellar Radius

[1]     In his book Our Undiscovered Universe (2007), Terence Witt assumes “that a black hole [as] heavy [as the mass of the Milky Way’s core, about three million times that of our sun,] can compress its innermost matter to hyperdensity  … [M]atter is not infinitely compressible … Black holes are not singularities, gravitational or otherwise, regardless of their size.  They are merely compact objects with deep gravitational potentials.”

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