Regularizations of solutions for charged dust distributions in the Einstein–Maxwell theory

Regularization of singular solutions for the static spherically symmetric extremally charged dust in the Majumdar-Papapetrou system has been investigated. Singularities are of such a type that solutions become physically unacceptable since physically relevant quantities (metric invariants) are singular as well. With a simple redefinition of the charge/energy distributions, these solutions can be regularized. A spectrum of solutions with a number of zero-nodes in the metric tensor is found, and it is shown that their regularization can be accomplished either by using a delta-shell, or a thick shell distribution of matter. The bifurcating behaviour of regular solutions is not present any more, but quantized-like behaviour in the total mass allocated to the solutions is observed.