Charged cosmological dust solutions of the coupled Einstein and Maxwell equations (original) (raw)

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

Canadian Journal of Physics

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 and (or) charge, the solutions have singularities of a type that 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 and (or) 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. The spectrum of regularized solutions restores the equality of the Tolman–Whittaker and Arnowitt–Deser–Misner (ADM) mass, as well the equality of the net charge and ADM mass, which is the distinctive feature of Majumdar–Papapetrou systems.PACS No.:04.40.Nr

Extremely Charged Static Dust Distributions in General Relativity

arXiv: General Relativity and Quantum Cosmology, 1998

Conformo static charged dust distributions are investigated in the framework of General Relativity. Einstein's equations reduce to a nonlinear version of Poisson's equations and Maxwell's eqations imply the equaltiy of the charge and mass densities. An interior solution to the extreme Reissner-Nordstrom metric is given. Dust distributions concentrated on regular surfaces are discussed and a complete solution is given for a spherical thin shell.