Unified Bertotti-Robinson and Melvin Spacetimes

TL;DR

This paper introduces a unified solution to Einstein-Maxwell equations that combines Bertotti-Robinson and Melvin spacetimes, revealing new features like singularities and inaccessible regions depending on magnetic field strength.

Contribution

The authors derive a single metric unifying BR and ML solutions, highlighting new geometric features and singularities not present in separate solutions.

Findings

Unified metric encompasses both BR and ML spacetimes.

Singularity formation on the symmetry axis at high magnetic fields.

Existence of regions inaccessible to null geodesics.

Abstract

We present a solution for the Einstein-Maxwell (EM) equations which unifies both the magnetic Bertotti-Robinson (BR) and Melvin (ML) solutions as a single metric in the axially symmetric coordinates ${t,\rho,z,\varphi} $. Depending on the strength of magnetic field the spacetime manifold, unlike the cases of separate BR and ML spacetime, develops singularity on the symmetry axis ($\rho =0$). Our analysis shows, beside other things that there are regions inaccessible to all null geodesics.