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

Abstract

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