Asymptotical quasinormal mode spectrum for piecewise approximate effective potential

Understand

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 asymptotical 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.