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arXiv · 2602.17581

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

José Barrientos·Adolfo Cisterna·Amaro Díaz·Keanu Müller
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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.

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José Barrientos, Adolfo Cisterna, Amaro Díaz, Keanu Müller. 2026-02-19. From Bertotti--Robinson to Vacuum: New Exact Solutions in General Relativity via Harrison and Inversion Symmetries. https://arxiv.org/abs/2602.17581

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