Charged black points in General Relativity coupled to the logarithmic U(1) gauge theory
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The exact solution for a static spherically symmetric field outside a charged point particle is found in a non-linear $U(1)$ gauge theory with a logarithmic Lagrangian. The electromagnetic self-mass is finite, and for a particular relation between mass, charge, and the value of the non-linearity coupling constant, $\lambda$, the electromagnetic contribution to the Schwarzschild mass is equal to the total mass. If we also require that the singularity at the origin be hidden behind a horizon, the mass is fixed to be slightly less than the charge. This object is a {\em black point.}
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