Novel (Non-)Accelerating Vacuum Spacetimes from Bertotti--Robinson Black Holes via Harrison and Inversion 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 employ two independent mechanisms: a Melvin--Bonnor-type magnetization and an Inversion symmetry of the Einstein--Maxwell system. In both cases the external electromagnetic field can be removed, while a non-trivial gravitational backreaction remains in the metric, yielding new accelerating vacuum spacetimes of Petrov type I. In the static, non-accelerating limit, the magnetized Schwarzschild case reproduces previously known results, whereas the Inversion symmetry leads to a genuinely new vacuum configuration. These findings provide a method for generating algebraically general vacuum geometries and illustrate how electromagnetic embeddings can produce non-trivial vacuum metrics in General Relativity. The main geometrical properties of these spacetimes are discussed. Two additional results are presented in the appendices: a stationary generalization of these vacuum geometries, and two further static vacuum configurations obtained through the same symmetries but using the Alekseev--García black hole as the seed.