Physical interpretation of the analytically continued charged solution

Determine the physical interpretation of the analytically continued Reissner–Nordström–Bertotti–Robinson–Bonnor–Melvin solution obtained by setting the Bertotti–Robinson parameter B to iB when the intrinsic monopolar charge e is nonzero.

Background

For vanishing intrinsic charge, the paper describes an analytic continuation B to iB that yields a real vacuum metric associated with a Schwarzschild black hole inside an expanding bubble of nothing. The authors then consider the charged case and find that the same continuation appears to produce complex metric and gauge-potential components.

Consequently, the physical meaning of this charged analytic continuation is left unresolved. The issue concerns the case e not equal to zero and is distinct from the uncharged continuation, whose interpretation is given.

References

When $e=0$ it is possible to analytically continue the solution by setting $B\to i B$, in this special case, to get a real vacuum metric describing a Schwarzschild black hole inside the expanding bubble of nothing , , . But when $e \ne 0$ the metric and gauge potential seems not to have only real components, therefore the physical interpretation is unclear.

Reissner-Nordstrom in the Bertotti-Robinson-Bonnor-Melvin electromagnetic field  (2609.00882 - Astorino, 1 Sep 2026) in Section 3.1, Special case: removal of the external magnetic field