Global extensions and causal structure of the broader family

Determine how acceleration and NUT-like twist affect maximal extensions, accessible singularities, and the causal roles of Killing horizons in the broader generalized black-hole family beyond the explicitly matched Kerr–Newman–Bertotti–Robinson subclasses.

Background

The paper explains that recent studies have constructed extensions across coordinate surfaces such as r=∞r=\infty for Kerr–Bertotti–Robinson and Kerr–Newman–Bertotti–Robinson geometries. The correspondence established in the paper allows those results to be transferred to certain non-accelerating, effective-NUT-free subclasses.

For the more general solutions containing acceleration and NUT-like twist, the maximal extensions and causal interpretation remain unresolved. In particular, it is not established which coordinate surfaces can be extended through, which singularities are accessible, or how the various Killing horizons function globally.

References

For the broader family, the remaining problem is to determine how acceleration and NUT-like twist affect these extensions, the accessible singularities, and the causal roles of the Killing horizons.

— Generalized Black holes with Fully Non-aligned Electromagnetic Fields  (2609.10332 - Furugori et al., 9 Sep 2026) in Section 10, Summary and discussion, paragraph “Global structure and horizon topology”

Notably, coordinate systems covering more causal blocks exist, e.g., for the Reissner-Nordström spacetime (see also for a recent generalization). Whether such a coordinate system (usually referred to as Israel coordinates) can be generalized to the case of COS diagrams for the Kerr metric remains, to our knowledge, an open problem.

— Kerr geodesics on conformal projection diagrams  (2610.09878 - Podleśny et al., 7 Oct 2026) in Section 2.2, “Compactification, conformal blocks”

It remains to be explored whether accelerating Kerr-(A)dS geometries admit the double-horizon limit leading to swirling backgrounds with cosmological constant.

— From Accelerating Rotating Black Holes to a Swirling Universe  (2610.21860 - Barrientos et al., 15 Oct 2026) in Section 3, Final remarks