No-go theorem for static configurations of two charged dust species

Abstract

Abstract We consider static spacetimes with no specific spacial symmetry where the matter content consists of two charged dust species. This comes motivated by the fact that static configurations are possible with one dust, but only if it is electrically counterpoised dust (ECD). In order to have such dust, the quotient between electric charge density and mass density needs to be fine-tuned to a value that is far less than the charge-mass quotient for any known particle. Here we prove that there are no static configurations with two dust species unless each one is ECD. This shows that ECD spacetimes cannot be made with matter that has on average the correct charge-mass ratio, but that the underlying particles must have such ratio.