TITLE:
Mathematical and Geometrical Inconsistency of the Black Hole Model. Part I
AUTHORS:
Jean-Pierre Petit, Gilles D’Agostini
KEYWORDS:
Black Hole, M87*, SgrA*, Birkhoff Theorem, Plugstar, Hilbert, Two Folds Cover Manifold, Bounded Manifold, PT-Symmetry, Geometrical Criticity, Physical Criticity, Mass Inversion, Negative Mass, Time Factor, Throat Sphere, Hoag galaxy, Density Wave, Supermassive Objects, Neutron Stars, Janus Cosmological Model
JOURNAL NAME:
Journal of Modern Physics,
Vol.17 No.2,
February
28,
2026
ABSTRACT: We show that the model of the black hole is a complete mathematical and geometrical chimera, born from wrong interpretations of the Schwarzschild external metric solution. The first misconception stems from Hilbert’s confusion of the Schwarzschild intermediate magnitude R with a radial coordinate r. The second arises from the omission of the cross term in drdt, which, by yielding a finite free-fall time, allowed Oppenheimer and Snyder in 1939 to suggest using a stationary solution to describe a highly unsteady phenomenon. The third is a consequence of the assumption of space contractibility, which creates the myth of the existence of the interior of black holes and a central singularity, with real spiral trajectories endowed with an imaginary length, thus located outside the hypersurface. This translates in the literature into the surreal idea that space and time coordinates exchange roles. Starting from the only accessible observational quantities, the images of the objects M87* and SgrA*, that is, a ratio of maximum to minimum brightness temperatures of 3, we show that this gravitational redshift effect then fits within the Schwarzschild inner metric solution when physical criticality is approached. The criticism formulated by Einstein in 1939 regarding this solution must be reconsidered, as the physical conditions in such criticality are such that the distances between baryons become on the order of their Compton length. Thus, the precise physical description of such states, and the suggested mass inversion process in objects described as plugstars, will require the completion of the unification between general relativity and quantum mechanics. As it stands, this reinterpretation of the Schwarzschild outer and inner solutions then fits into the Janus Cosmological Model. It is predicted that all future objects of this type will exhibit this same ratio of 3 and that the masses of neutron stars are less than 2.5 solar masses, therefore, in general, black holes of any size simply do not exist. It is suggested that the supermassive objects M87* and Sgr A* result from the implosion of density waves similar to those in Hoag’s Galaxy.