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We extend the discussion of the antipodal identification of black holes tothe Reissner-Nordstr\"om (RN) spacetime by developing the classical toolsnecessary to define the corresponding quantum field theory (QFT). We solve themassless Klein-Gordon equation in the RN background in terms of scatteringcoefficients and provide a procedure for constructing a solution for anarbitrary analytic extension of RN. The behavior of the maximally extendedsolution is highly dependent upon the coefficients of scattering between theinner and outer horizons, so we present the low-frequency behavior of, andnumerical solutions for, these quantities. We find that, for low enoughfrequency, field amplitudes of solutions with purely positive or negativefrequency at each horizon will acquire only a phase after passing both theinner and outer horizons, while at higher frequencies the amplitudes will tendto grow exponentially either to the future or to the past, and decayexponentially in the other direction. Regardless, we can always construct abasis of globally antipodal symmetric and antisymmetric solutions for anyfinite analytic extension of RN. We have characterized this basis in terms ofpositive and negative frequency solutions for future use in constructing thecorresponding QFT.

Classical Tools for Antipodal Identification in Reissner-Nordstr\"om Spacetime