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Regular and singular solutions for charged dust distributions in the Einstein--Maxwell theory

Dubravko Horvat·Sasa Ilijic
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Abstract

Solutions for the static spherically symmetric extremally charged dust in the Majumdar--Papapetrou system have been found. For a certain amount of the allocated mass/charge, the solutions have singularities of a type which could render them physically unacceptable, since the corresponding physically relevant quantities are singular as well. These solutions, with a number of zero-nodes in the metric tensor, are regularized through the $δ$-shell formalism, thus redefining the mass/charge distributions. The bifurcating behaviour of regular solutions found before is no longer present in these singular solutions, but quantized-like behaviour in the total mass is observed. Spectrum of regularized solutions restores the equality of the Tolman--Whittaker and ADM mass, as well the equality of the net charge and ADM mass, which is the distinctive feature of Majumdar--Papapetrou systems.

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Dubravko Horvat, Sasa Ilijic. 2007-09-28. Regular and singular solutions for charged dust distributions in the Einstein--Maxwell theory. https://doi.org/10.1139/p07-090

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