On the black hole limit of electrically counterpoised dust configurations

Abstract

By means of a simple scaling transformation any asymptotically flat Papapetrou–Majumdar solution of the Einstein–Maxwell equations corresponding to a localized regular distribution of electrically counterpoised dust can be reformulated as a one-parameter family of solutions admitting a black hole limit. In the limit, a characteristic separation of spacetimes occurs. From the exterior point of view, the extreme Reissner–Nordström metric outside the event horizon is formed. From the interior point of view, a regular, non-asymptotically flat (and in general non-spherically symmetric) spacetime with the extreme Reissner–Nordström near-horizon geometry at spatial infinity results.