Charged cosmological dust solutions of the coupled Einstein and Maxwell equations

TL;DR

This paper explores continuous distributions of extremely charged dust in Einstein-Maxwell theory, extending known blackhole solutions to smooth, asymptotically flat spacetimes with finite mass.

Contribution

It introduces a new class of smooth, continuous solutions modeling extended charged dust distributions, generalizing point charge solutions.

Findings

Existence of smooth solutions for finite ADM mass distributions.

Asymptotically flat spacetime metrics achieved.

Extension of blackhole solutions to continuous matter distributions.

Abstract

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.