Black-hole normal modes: A WKB approach. I. Foundations and application of a higher-order WKB analysis of potential-barrier scattering

Stability and thermodynamics of brane black holes

“…In order to analyze quasinormal mode phase and latetime behavior of the perturbations, we apply a numerical characteristic integration scheme based in the light-cone variables u = t − r ⋆ and v = t + r ⋆ used, for example, in [26,27,28]. In addition, to check some results obtained in "time-dependent" approach we employ the semi-analytical WKB-type method developed in [29] and improved in [30]. Both approaches show good agreement for the fundamental overtone which is the dominating contribution in the signal for intermediate late-time.…”

Split fermion quasinormal modes

“…To evaluate the QNM frequencies we adopt the WKB approximation developed by Iyer and Will [15], also see references therein. Note that this analytic method has been used extensively in various BH cases [16], where comparisons with other numerical results have been found to be accurate up to around 1% for both the real and the imaginary parts of the frequencies for low-lying modes with n < l (where n is the mode number and l is the spinor angular momentum quantum number).…”

Quasinormal modes of charged, dilaton black holes

“…We have computed the complex frequencies of the quasi-normal modes associated to the axial and polar wave equation by using a WKB approximation devised by Schutz and Will [15] and extended to higher orders by Iyer and Will [16]. This approach has been applied to the Schwarzchild [17] and Reissner Nordström [18] cases, and for the fundamental quadrupole mode l = 2 agrees with other approaches [19] within 1% both for the real and the immaginary parts of the first 3-4 modes.…”

“…[13] are corrected and the explicit expression of the matrix whose eigenvalues are the potentials governing polar perturbations is given in the Appendix. In Section 5 the quasi-normal frequencies of the GHS black hole obtained with an extended WKB approch [16] are calculated for different values of the parameters. Finally, in Section 6 the results obtained are discussed and the main qualitative differences between the spectra of the dilaton and the Reissner Nordström black holes are pointed out.…”