No-go theorem for static spherically symmetric configurations composed of two charged pressureless fluid species

TL;DR

This paper proves that static, spherically symmetric configurations of two charged dust fluids in equilibrium are impossible unless they are identical in charge-to-mass ratio, across Newtonian, relativistic, and general relativistic frameworks.

Contribution

It establishes a no-go theorem for two charged dust species in equilibrium, extending the result across multiple theories of mechanics.

Findings

Two charged dust fluids cannot be in equilibrium unless identical in charge-to-mass ratio.

Charged dust solutions cannot form black hole mimickers unless the charge-to-mass ratio is correct.

The theorem applies in Newtonian, Special Relativity, and General Relativity.

Abstract

We present a no-go theorem for spherically symmetric configurations of two charged fluid species in equilibrium. The fluid species are assumed to be dusts, that is, perfect fluids without pressure, and the equilibrium can be attained for a single dust from the balance of electrostatic repulsion and gravitational attraction. We show that this is impossible for two dust species unless both of them are indistinguishable in terms of their electric charge density to matter density ratio. The result is obtained in the main three theories of mechanics, that is, in Newtonian Mechanics, in Special Relativity and in General Relativity. In particular, as charged dust solutions have been used to study the possibility of black hole mimickers, this result shows that such mimickers can not be constructed unless the underlying charged particle has the correct charge to mass ratio.