On the asymptotic distribution of quasinormal-mode frequencies for Schwarzschild black holes

The highly damped quasinormal-mode frequencies of Schwarzschild black holes are discussed. Numerical results obtained from a phase-integral formula derived by Andersson and Linnaeus (1992) are compared with the predictions of an approximate formula given by Nollert (1990). Close agreement between the two independent methods suggests that reliable conclusions regarding the asymptotic behaviour of the quasinormal-mode frequencies may be drawn. For a Schwarzschild black hole with mass M the physical oscillation frequency approaches the asymptotic value (in geometrized units) 0.0437 M-1. Meanwhile, the characteristic damping of the modes increases linearly with the integer index labelling the modes. The asymptotic behaviour is independent of the angular harmonic index l.