In physics, there is a speculative hypothesis that, if there were a black hole with the same mass, charge and angular momentum as an electron, it would share other properties of the electron. Most notably, Brandon Carter showed in 1968 that the magnetic moment of such an object would match that of an electron.[1] This is interesting because calculations ignoring special relativity and treating the electron as a small rotating sphere of charge give a magnetic moment roughly half the experimental value (see Gyromagnetic ratio).
However, Carter's calculations also show that a would-be black hole with these parameters would be "super-extremal". Thus, unlike a true black hole, this object would display a naked singularity, meaning a singularity in spacetime not hidden behind an event horizon. It would also give rise to closed timelike curves.
Standard quantum electrodynamics (QED), currently the most comprehensive theory of particles, treats the electron as a point particle. There is no evidence that the electron is a black hole (or naked singularity) or not. Furthermore, since the electron is quantum-mechanical in nature, any description purely in terms of general relativity is paradoxical until a better model based on understanding of quantum nature of blackholes and gravitational behaviour of quantum particles is developed by research. Hence, the idea of a black hole electron remains strictly hypothetical.
^Carter, B. (25 October 1968). "Global structure of the Kerr family of gravitational fields". Physical Review. 174 (5): 1559–1571. Bibcode:1968PhRv..174.1559C. doi:10.1103/physrev.174.1559.
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