Researchers have formulated and numerically solved the scattering problem for a neutral, minimally coupled, massless scalar particle in the Kerr-Bertotti-Robinson (Kerr-BR) black hole geometry. These black holes, which feature an external magnetic field, differ from asymptotically flat ones in that their coordinate "infinity" lies at a finite tortoise distance. The study reveals that the resulting reflection data are conditional on the imposed boundary prescription, suggesting that the cross-section is not unique or observer-independent in this context.

The wave equation for the scalar field, due to the traceless Maxwell stress tensor of the background, reduces to the four-dimensional conformal wave equation. This allows for a Carter-like separation of variables after scaling the scalar field by the conformal factor. The open-channel superradiance phenomenon in this model is governed by a "double-gate" mechanism, requiring both the local horizon condition and an outer propagation condition (q_infinity^2 > 0).

A crucial finding is that, at a benchmark spin of a/M=0.9, the co-rotating dipole amplification decreases as the external magnetic field strength increases. Specifically, the magnetic field narrows and eventually closes the open superradiant window at approximately BM=0.243. Near the propagation threshold, the amplification coefficient vanishes linearly with the outer wave number. These results offer new insights into the interaction between scalar fields and black holes in the presence of magnetic fields.