Simple derivation of quasinormal modes for arbitrary spins (Q2495127)

Two various approaches are developed to calculate the leading approximation of the quasinormal modes of a Schwarzschild Black Hole for spins \(s=0,1/2,1,2\). The first one is based on the Regge-Wheeler formalism, while the second one uses a closed contour in a complex \(r\)-plane. In the case of spin 1/2 field the result obtained coincides with the numerical calculations by \textit{J. Jing} [Phys. Rev. D 71, 124006 (2005), see also gr-qc/0502023] and differs from the result of analytical calculations obtained by \textit{K. H. C. Castello-Branco, R. A. Konoplya}, and \textit{A. Zhidenko} [Phys. Rev. D 71, 047502 (2005), see also hep-th/0411055]. As a historical remark, the reviewer is mentioning, that the equations (6) and (7) were examined for the first time by \textit{J. A. Wheeler} [in ``Transcending the law of conservation of leptons'', Q. Acad. Naz. Lincei 368 No. 157, 133--164] for spin 0 and 1/2 particles and by \textit{A. A. Kharkov} [in: ``Electromagnetic fields near massive rotating stars'' (Russian). Novosibirsk, 1972. Preprint INP 73-72] for spin 1 for slightly other boundary conditions. Wheeler showed, that there is non-null absorption of quantum fields by a black hole in the long-wavelength limit, while Kharkov calculated explicitely the transmission coefficient for electromagnetic waves by a black hole in the same limit.