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.