Quasi-normal modes correspond to pure tones of the black hole. It describes for arbitrary, but small, perturbations such as an object falling into the black hole, accretion of matter surrounding it, last stage of slightly aspherical collapse etc. Unlike the reflection and transmission coefficient problem, quasi-normal modes are characterised by complex-valued σ σ 's with the convention R e { σ σ } > 0 . The required boundary conditions are