Construction of Sources for Majumdar-Papapetrou Spacetimes

TL;DR

This paper constructs non-singular, physically plausible sources for Majumdar-Papapetrou spacetimes using new parameters and symmetries, enhancing understanding of charged dust solutions in Einstein-Maxwell theory.

Contribution

It introduces a novel method for constructing smooth, singularity-free sources for Majumdar-Papapetrou solutions utilizing new parameters and non-Noetherian symmetries.

Findings

Derived class C^1, singularity-free geometries.

Identified redshift differences for bounded and unbounded sources.

Linked conformastatic metrics with homothetic and collineation symmetries.

Abstract

We study Majumdar-Papapetrou solutions for the 3+1 Einstein-Maxwell equations, with charged dust acting as the external source for the fields. The spherically symmetric solution of G\"{u}rses is considered in detail. We introduce new parameters that simplify the construction of class $C^1$, singularity-free geometries. The arising sources are bounded or unbounded, and the redshift of light signals allows an observer at spatial infinity to distinguish these cases. We find out an interesting affinity between the conformastatic metric and some homothetic, matter and Ricci collineations. The associated non-Noetherian symmetries provide us with distinctive solutions that can be used to construct non-singular sources for Majumdar-Papapetrou spacetimes.}