Thin static charged dust Majumdar-Papapetrou shells with high symmetry in D >= 4

TL;DR

This paper systematically studies high-symmetry static D≥4 spacetimes with thin charged dust shells, providing general solutions to Einstein-Maxwell equations, analyzing flat interior solutions especially in D=4, and discussing extensions to Kastor-Traschen spacetimes with cosmological constant.

Contribution

It offers a comprehensive solution framework for static high-symmetry charged dust shells in D≥4, including special cases and generalizations to Kastor-Traschen spacetimes.

Findings

Derived general solutions to Einstein-Maxwell equations for these shells.

Analyzed flat interior solutions specifically in four dimensions.

Discussed possible extensions to include a cosmological constant.

Abstract

We present a systematical study of static D >= 4 space-times of high symmetry with the matter source being a thin charged dust hypersurface shell. The shell manifold is assumed to have the following structure S_(beta) X R^(D-2-beta), beta (in the interval <0,...,D-2>) is dimension of a sphere S_(beta). In case of (beta) = 0, we assume that there are two parallel hyper-plane shells instead of only one. The space-time has Majumdar-Papapetrou form and it inherits the symmetries of the shell manifold - it is invariant under both rotations of the S_(beta) and translations along R^(D-2-beta). We find a general solution to the Einstein-Maxwell equations with a given shell. Then, we examine some flat interior solutions with special attention paid to D = 4. A connection to D = 4 non-relativistic theory is pointed out. We also comment on a straightforward generalisation to the case of Kastor-Traschen space-time, i.e. adding a non-negative cosmological constant to the charged dust matter source.