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Célérier, M.N., Santos, N.O. and Satheeshkumar, V.H. (2017) Hilbert Repulsion in the Reissner-Nordström and Schwarzschild spacetimes. arXiv: 1707.06994.

has been cited by the following article:

• TITLE: Sources of Very High and Ultra High Energy Cosmic Ray Protons

  AUTHORS: Charles H. McGruder III

  KEYWORDS: Cosmic Ray Protons, General Relativity, Gravitational Repulsion, Schwarzschild Field

  JOURNAL NAME: Journal of Modern Physics, Vol.17 No.4, April 27, 2026

  ABSTRACT: We employ the theory of gravitational repulsion in the Schwarzschild field to show that neither Active Galactic Nuclei (AGN) nor main sequence stars are the sources of ultra high energy cosmic ray protons. Instead the theory leads to the conclusion that the sources of these particles are brown dwarfs except for protons with energies >1.887×1020 eV, which are produced by planetary mass bodies. The theory predicts that brown dwarfs and main sequence stars are the sources of very high energy cosmic ray protons.