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It is well known through the work of Majumdar, Papapetrou, Hartle, andHawking that the coupled Einstein and Maxwell equations admit a static multipleblackhole solution representing a balanced equilibrium state of finitely manypoint charges. This is a result of the exact cancellation of gravitationalattraction and electric repulsion under an explicit condition on the mass andcharge ratio. The resulting system of particles, known as an extremely chargeddust, gives rise to examples of spacetimes with naked singularities. In thispaper, we consider the continuous limit of theMajumdar--Papapetrou--Hartle--Hawking solution modeling a space occupied by anextended distribution of extremely charged dust. We show that for a givensmooth distribution of matter of finite ADM mass there is a continuous familyof smooth solutions realizing asymptotically flat space metrics.

Charged cosmological dust solutions of the coupled Einstein and Maxwell equations