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The Kerr-Newman Horizon Condition for the Electron

Author: Egor Nikiforov


Abstract

The aim of this report is to investigate whether the electron can satisfy the horizon condition of a Kerr-Newman black hole. Since the electron has mass, spin, and electric charge, its physical parameters can be formally compared with the classical black-hole condition. After converting the electron's mass, charge, and spin into geometrized units, the calculation shows that the electron does not satisfy the black-hole condition because its spin and charge are very large compared with its gravitational mass. As a result, the electron cannot be described as a classical black hole. This illustrates why classical general relativity should be applied to quantum particles only with caution.


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References

[1] L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, Course of Theoretical Physics, Vol. 2, 4th ed., Butterworth-Heinemann, Oxford (1980).

[2] C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation, W. H. Freeman, San Francisco (1973).

[3] R. M. Wald, General Relativity, University of Chicago Press, Chicago (1984).

[4] D. J. Griffiths and D. F. Schroeter, Introduction to Quantum Mechanics, 3rd ed., Cambridge University Press, Cambridge (2018).

[5] S. Navas et al. (Particle Data Group), Review of Particle Physics, Physical Review D 110, 030001 (2024). 10.1103/PhysRevD.110.030001

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