From Bertotti--Robinson to Vacuum: New Exact Solutions in General Relativity via Harrison and Inversion Symmetries

TL;DR

This paper develops a systematic method to generate new algebraically general vacuum solutions in General Relativity by exploiting symmetries of electrovacuum configurations, revealing novel accelerating and static vacuum spacetimes.

Contribution

It introduces new vacuum solutions derived from electrovacuum backgrounds using Harrison and Inversion symmetries, extending known geometries and providing a framework for generating algebraically general vacuum metrics.

Findings

New accelerating vacuum spacetimes of Petrov type I constructed.

A two-parameter extension of Schwarzschild--Levi-Civita geometry found.

Stationary and static vacuum configurations derived from symmetries.

Abstract

We construct new vacuum solutions of the Einstein equations generated from electrovacuum configurations embedded in external electromagnetic backgrounds. Starting from accelerating Bertotti--Robinson black holes, we exploit two independent symmetries of the electrovacuum: a Melvin--Bonnor-type magnetization and a magnetic Inversion. In both constructions, the external electromagnetic field can be removed while still leaving a non-trivial gravitational backreaction in the metric, yielding new accelerating vacuum spacetimes of Petrov type I. In the static, non-accelerating limit, the magnetized Bertotti--Robinson--Schwarzschild case reproduces known results, while the Inversion symmetry produces a genuinely new vacuum configuration, a two-parameter extension of the Schwarzschild--Levi-Civita geometry. These constructions provide a systematic method for generating algebraically general vacuum geometries and illustrate how electromagnetic embeddings can induce non-trivial vacuum metrics in General Relativity. The main geometrical properties of these spacetimes are analyzed. Additionally, we present two further results: a stationary generalization of these vacuum geometries and two new static vacuum configurations obtained by applying the same symmetries to the Alekseev--Garc\'ia black hole seed.