  It is well known through the work of Majumdar, Papapetrou, Hartle, and
Hawking that the coupled Einstein and Maxwell equations admit a static multiple
blackhole solution representing a balanced equilibrium state of finitely many
point charges. This is a result of the exact cancellation of gravitational
attraction and electric repulsion under an explicit condition on the mass and
charge ratio. The resulting system of particles, known as an extremely charged
dust, gives rise to examples of spacetimes with naked singularities. In this
paper, we consider the continuous limit of the
Majumdar--Papapetrou--Hartle--Hawking solution modeling a space occupied by an
extended distribution of extremely charged dust. We show that for a given
smooth distribution of matter of finite ADM mass there is a continuous family
of smooth solutions realizing asymptotically flat space metrics.
