The charged dust solution of Ruban -- matching to Reissner--Nordstr\"om and shell crossings

TL;DR

This paper explores matching a charged dust solution by Ruban to Reissner--Nordstr"om spacetime, analyzing conditions to avoid shell crossings and maintain a consistent wormhole-like structure.

Contribution

It demonstrates how Ruban's charged dust solution can be matched to RN spacetime, highlighting the limitations imposed by shell crossings on oscillatory behavior.

Findings

Matching is possible with the RN solution between the horizons.

Shell crossings prevent full oscillations of the dust shell.

The solution's behavior is constrained by the presence of shell crossings.

Abstract

The maximally extended Reissner--Nordstr\"om (RN) manifold with $e^2 < m^2$ begs for attaching a material source to it that would preserve the infinite chain of asymptotically flat regions and evolve through the wormhole between the RN singularities. So far, the attempts were discouraging. Here we try one more possible source -- a solution found by Ruban in 1972 that is a charged generalisation of an inhomogeneous Kantowski--Sachs-type dust solution. It can be matched to the RN solution, and the matching surface must stay all the time between the two RN event horizons. However, shell crossings do not allow even half a cycle of oscillation between the maximal and the minimal size.