  To find the pair production, absorption cross section and quasi-normal modes
in background fields, we advance the monodromy method that makes use of the
regular singular points of wave equations. We find the mean number of pairs
produced in background fields whose mode equations belong to the Riemann
differential equation and apply the method to the three particular cases: (i)
charges near the horizon of near-extremal black holes, (ii) charges with
minimal energy under the static balance in nonextremal charged black holes, and
(iii) charges in the Sauter-type electric fields. We then compare the results
from the monodromy with those from the exact wave functions in terms of the
hypergeometric functions with three regular singular points. The explicit
elaboration of monodromy and the model calculations worked out here seem to
reveal evidences that the monodromy may provide a practical technique to study
the spontaneous pair production in general black holes and electromagnetic
fields.
