Asymptotical quasinormal mode spectrum for piecewise approximate effective potential

It was pointed out that the black hole quasinormal modes resulting from a piecewise approximate potential are drastically distinct from those pertaining to the original black hole metric. In particular, instead of lining up parallel to the imaginary axis, the spectrum is found to stretch out along the real axis. In this work, we prove that if there is a single discontinuity in the effective potential, no matter how insignificant it is, the asymptotic behavior of the quasinormal modes will be appreciably modified. Besides showing numerical evidence, we give analytical derivations to support the above assertion even when the discontinuity is located significantly further away from the maximum of the potential and/or the size of the step is arbitrarily small. Moreover, we discuss the astrophysical significance of the potential implications in terms of the present findings.

Automated summary

The black hole quasinormal modes resulting from a piecewise approximate potential are drastically different from those of the original black hole metric, with the spectrum stretching out along the real axis instead of lining up parallel to the imaginary axis. Even a slight discontinuity in the effective potential significantly modifies the asymptotic behavior of the quasinormal modes, as supported by analytical derivations. Additionally, the astrophysical implications of these findings are discussed.