Global coordinates or a larger global description for massive KBR spacetime

Construct global coordinates or otherwise determine a larger global description of the Kerr–Bertotti–Robinson spacetime for nonzero mass parameter M, potentially resolving the coordinate degeneration and Maxwell-field obstruction associated with the axial Ω=0 locus.

Background

For M=0, the Kerr–Bertotti–Robinson geometry reduces to Bertotti–Robinson spacetime, for which global coordinates are known and the apparent repeated extensions across r=∞ are understood as transitions between patches of a single global geometry. The authors note that no analogous global coordinates are available for M≠0.

They examine a coordinate transformation near the axial Ω=0 locus, which locally produces a Bertotti–Robinson-like form, but explain that the transformation cannot be extended globally because its Jacobian degenerates at specified points and because the Maxwell field has a nontrivial continuation. Thus, the infinite-chain extension is presented as a natural option, while a broader global description remains unresolved.

References

Our discussion has focused primarily on the common exterior region between the two black holes. The geometry inside each horizon is expected to retain the local structure found in the previous extensions of $\text{KBR}_\text{s}$ and KNBR. However, the previous global landscape, in which the interiors of the two black holes were glued to each other, should be abandoned. For the present two-black-hole interpretation, these interiors remain distinct and may admit independent global completions. A systematic analysis of these possible interior completions is left for future work.

— On the Extended Kerr-Newman-Bertotti-Robinson Spacetime: Two Black Holes and a Naked Singularity in Bertotti-Robinson Universe  (2609.20626 - Zhou et al., 17 Sep 2026) in Section 4, Conclusion and Discussion

The KNBR geometry is qualitatively different because its black holes need not be extremal. It therefore provides a considerably broader setting for multi-black-hole geometries with BR asymptotics and may hint at a related decoupling interpretation, although whether an asymptotically flat completion exists remains open.

— On the Extended Kerr-Newman-Bertotti-Robinson Spacetime: Two Black Holes and a Naked Singularity in Bertotti-Robinson Universe  (2609.20626 - Zhou et al., 17 Sep 2026) in Section 4, Conclusion and Discussion

Nevertheless, for $M\neq0$, no analogous global coordinates are known.

— Notes on Kerr-Bertotti-Robinson Spacetime  (2608.19136 - Zhou et al., 19 Aug 2026) in Conclusion and Discussion, paragraph beginning “We now turn to other possible extensions”

In principle, there may exist an alternative way to extend the spacetime across $r\to +\infty$ that ends with the conformal boundary and does not lead to an infinite number of parallel universes.

— Global structure of Kerr-Newman-BR spacetime  (2608.28265 - Ovcharenko, 28 Aug 2026) in Section Conclusions