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Charged regular black holes and Heisenberg-Euler nonlinear electrodynamics

By Mohammad Bagher Jahani Poshteh and Nematollah Riazi


A regular black hole solution of General Relativity coupled to a new model for nonlinear electrodynamics is presented. This model has the interesting feature that, at far distances from the black hole, the theory reduces to Maxwell electrodynamics with Heisenberg-Euler correction term. The singular center of the black hole is replaced by flat, de Sitter, or anti de Sitter space, if the spacetime in which the black hole is embedded is asymptotically flat, de Sitter, or anti de Sitter, respectively. We show that weak, as well as dominant and strong energy conditions are partially satisfied. They are violated in the region near the center of the black hole, which would be dressed up by an event horizon. Requiring the correspondence to Heisenberg-Euler Lagrangian at far distances, we find that in our model: (i) electron cannot be regarded as a regular black hole. (ii) A minimum mass is required for the formation of an event horizon. Stellar-mass charged black objects fail to provide this minimum. And, (iii) the mass of the black hole must be quantized.Comment: 5 pages, 3 figure

Topics: High Energy Physics - Theory, General Relativity and Quantum Cosmology
Year: 2020
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