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

Abstract

We consider static spacetimes with no specific spacial symmetry where thematter content consists of two charged dust species. This comes motivated bythe fact that static configurations are possible with one dust, but only if itis electrically counterpoised dust. In order to have such dust, the quotientbetween electric charge density and mass density needs to be fine-tuned to avalue 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 speciesunless each one is electrically counterpoised dust. This shows thatelectrically counterpoised dust spacetimes can not be made with matter that hason average the correct charge-mass ratio, but that the underlying particlesmust have such ratio.