Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 1 (2005), 013, 6 pages      http://dx.doi.org/10.3842/SIGMA.2005.013

Simple Derivation of Quasinormal Modes for Arbitrary Spins

Iosif Khriplovich and Gennady Ruban
Budker Institute of Nuclear Physics, 630090 Novosibirsk, Russia

Received October 07, 2005, in final form November 05, 2005; Published online November 07, 2005

Abstract
The asymptotically leading term of quasinormal modes (QNMs) in the Schwarzschild background, wn = - in/2, is obtained in two straightforward analytical ways for arbitrary spins.

Key words: Regge-Wheeler equation; quasinormal modes.

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References

  1. Regge T., Wheeler J.A., Stability of a Schwarzschild singularity, Phys. Rev., 1957, V.108, 1063-1069.
  2. Zerilli F.J., Gravitational field of a particle falling in a Schwarzschild geometry analyzed in tensor harmonics, Phys. Rev. D, 1970, V.2, 2141-2160.
  3. Vishveshwara C.V., Scattering of gravitational radiation by a Schwarzschild black hole, Nature, 1970, V.227, 936-938.
  4. Press W.H., Long wave trains of gravitational waves from a vibrating black hole, Astrophys. J., 1971, V.170, L105.
  5. Leaver E.W., An analytic representation for the quasi-normal modes of Kerr black holes, Proc. Roy. Soc. London Ser. A, 1985, V.402, 285-298.
  6. Nollert H.-P., Quasinormal modes of Schwarzschild black holes: the determination of quasinormal frequencies with very large imaginary parts, Phys. Rev. D, 1993, V.47, 5253-5258.
  7. Hod S., Bohr's correspondence principle and the area spectrum of quantum black holes, Phys. Rev. Lett., 1998, V.81, 4293-4296, gr-qc/9812002.
  8. Motl L., An analytical computation of asymptotic Schwarzschild quasinormal frequencies, Adv. Theor. Math. Phys., 2002, V.6, 1135-1162, gr-qc/0212096.
  9. Motl L., Neitzke A., Asymptotic black hole quasinormal frequencies, Adv. Theor. Math. Phys., 2003, V.7, 307-330, hep-th/0301173.
  10. Khriplovich I.B., Quasinormal modes, quantized black holes, and correspondence principle, Int. J. Mod. Phys. D, 2005, V.14, 181-183, gr-qc/0407111.
  11. Castello-Branco K.H.C., Konoplya R.A., Zhidenko A., High overtones of Dirac perturbations of a Schwarzschild black hole, Phys. Rev. D, 2005, V.71, 047502, 4 pages, hep-th/0411055.
  12. Jing J., Dirac quasinormal modes of Schwarzschild black hole, Phys. Rev. D, 2005, V.71, 124006, 7 pages, gr-qc/0502023.
  13. Padmanabhan T., Quasi normal modes: a simple derivation of the level spacing of the frequencies, Class. Quant. Grav., 2004, V.21, L1-L6, gr-qc/0310027.
  14. Medved A.J.M., Martin D., Visser M., Dirty black holes: quasinormal modes, Class. Quant. Grav., 2004, V.21, 1393-1405, gr-qc/0310009.
  15. Roy Chaudhury T., Padmanabhan T., Quasinormal modes in Schwarzschild-de Sitter spacetime: a simple derivation of the level spacing of the frequencies, Phys. Rev. D, 2004, V.69, 064033, 9 pages, gr-qc/0311064.
  16. Gradshteyn I.S., Ryzhik I.M., Table of integrals, series and products, New York, Academic Press, 1994.

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