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The proper understanding of the electromagnetic counterpart of gravity-wavesemitters is of serious interest to the multimessenger astronomy. In thisarticle, we study the numerical stability of the quasinormal modes (QNM) andquasibound modes (QBM) obtained as solutions of the Teukolsky Angular Equationand the Teukolsky Radial Equation with appropriate boundary conditions. We usethe epsilon-method for the system featuring the confluent Heun functions tostudy the stability of the spectra with respect to changes in the radialvariable. We find that the QNM and QBM are stable in certain regions of thecomplex plane, just as expected, while the third "spurious" spectrum was foundto be numerically unstable and thus unphysical. This analysis shows theimportance of understanding the numerical results in the framework of thetheory of the confluent Heun functions, in order to be able to distinguish thephysical spectra from the numerical artifacts.

Numerical stability of the electromagnetic quasinormal and quasibound modes of Kerr black holes