Melvin universe as a limit of the C-metric

TL;DR

The paper shows how the Melvin universe, a spacetime with a uniform electric field, can be derived as a limit of the C-metric describing two accelerated charged black holes, analyzing geometric quantities during this process.

Contribution

It introduces a new limiting procedure connecting the C-metric to the Melvin universe, providing insights into their geometric relationship.

Findings

Melvin universe obtained from the C-metric via a specific limit

Invariant geometric quantities studied during the limiting process

Clarifies the connection between black hole spacetimes and uniform electric fields

Abstract

It is demonstrated that the Melvin universe representing the spacetime with a strong 'homogeneous' electric field can by obtained from the spacetime of two accelerated charged black holes by a suitable limiting procedure. The behavior of various invariantly defined geometrical quantities in this limit is also studied.