Alice and Bob are hovering at say 10Rs at opposite sides of the non-rotarting black hole. Bob drops charged body and it is free falling into black hole (again, at opposite side from Alice). They both measure the intensity of electromagnetc field. Initially, of course, intensity at Bobs location is much higher. Question: do Alice and Bobs measurements become equal in finite time (as Black Hole does not have hair and it cant have any non-symemtric charge distribution), or, as for Bob and Alce object 'freezes' at the event horizon, Bob measures slightly more intensive EM field forever? My bet is they never become equal: even body reaches the singularity and situation becomes symmetric, the change in EM field propagates from EH very slowly. Now slightly different situation: Bob and Alice observe neutron star with non-symmetric charge distribution, where the unbalanced charge is already below future horizon. Now star suddenly collapses. I conclude that Bob and Alice wll still measure different values. Am I right?