On the black hole limit of electrically counterpoised dust configurations

TL;DR

This paper demonstrates how a family of solutions describing electrically counterpoised dust can transition into a black hole limit, revealing a separation of spacetime regions with distinct geometries.

Contribution

It introduces a simple scaling transformation that connects regular dust solutions to black hole configurations within Einstein-Maxwell theory.

Findings

Formation of an extreme Reissner-Nordstrom black hole in the limit

Interior spacetime remains regular and non-asymptotically flat

Exterior spacetime approaches the extreme Reissner-Nordstrom metric

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-Nordstrom 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-Nordstrom near-horizon geometry at spatial infinity results.