Quasinormal modes of charged fields in Reissner-Nordström backgrounds by Borel-Padé summation of Bender-Wu series
Dan Stefan Eniceicu, Matthew Reece
Abstract
We extend recent work of Hatsuda on the computation of quasinormal mode frequencies via analytic continuation of bound state energies and Borel-Pad\'e resummation of the Bender-Wu perturbation series to the case of charged fields in the background of Reissner-Nordstr\"om black holes. We compare the quasinormal mode frequencies obtained in this manner to calculations using Leaver's method of continued fractions, and find good agreement for damped modes with the imaginary part remaining finite in the extremal limit. We also present numerical evidence that the frequencies of certain zero-damped modes with the imaginary part tending to zero in the extremal limit can be computed when constructing the Bender-Wu expansion about a peak of the potential inside the outer horizon of the black hole.