General Relativity and Gravitation

, Volume 18, Issue 9, pp 913–921 | Cite as

Normal modes of a model radiating system

  • Kostas D. Kokkotas
  • Bernard F. Schutz
Research Articles


In order to gain insight into normal modes of realistic radiating systems, we study the simple model problem of a finite string and a semi-infinite string coupled by a spring. As expected there is a family of modes which are basically the modes of the finite string slowly damped by the “radiation” of energy to infinity on the semi-infinite string. But we also study another family of modes, found by Dyson in a different model problem, which are strongly damped modes of the semi-infinite string itself. These may be analogous to the modes of black holes, and they are likely to be present in relativistic stars as well. The question of whether the instability in these modes which Dyson found is present in realistic stars remains open.


Radiation Black Hole Simple Model Normal Mode Differential Geometry 
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  1. 1.
    Schutz, B. F. (1984). InRelativistic Astrophysics and Cosmology, X. Fustero and E. Verdaguer, eds. (World Scientific, Singapore), pp. 35–97.Google Scholar
  2. 2.
    Balbinski, E., Detweiler, S. L., Lindblom, L., and Schutz, B. F. (1985).Mon. Not. Roy. Astron. Soc.,213, 553.Google Scholar
  3. 3.
    Dyson, J. F. (1980). Ph. D. Thesis, University of Wales. (Dyson's model is based on one proposed by J. L. Anderson.)Google Scholar
  4. 4.
    Dixon, J. F. (1980). InProceedings of the Third Gregynog Relativity Workshop, M. Walker, ed. (MPI-PAE/Astro 204), p. 7.Google Scholar
  5. 5.
    Stewart, J. M. (1983).Gen. Rel. Grav.,15, 425.Google Scholar
  6. 6.
    Anderson, J. L. (1985). Private communication.Google Scholar
  7. 7.
    Thorne, K. S. (1969).Astrophys. J.,158, 997.Google Scholar
  8. 8.
    Thorne, K. S., and Campollataro, A. (1967).Astrophys. J.,148, 551.Google Scholar
  9. 9.
    Chandrasekhar, S., and Detweiler, S. (1975).Proc. Roy. Soc. London Ser. A,344, 441.Google Scholar
  10. 10.
    Schutz, B. F., and Will, C. M. (1985).Astrophys. J.,291, L33.Google Scholar
  11. 11.
    Comins, N., and Schutz, B. F. (1978).Proc. Roy. Soc. London Ser. A,364, 211.Google Scholar
  12. 12.
    Friedman, J. L., and Schutz, B. F. (1975).Astrophys. J.,200, 204.Google Scholar
  13. 13.
    Friedman, J. L., and Schutz, B. F. (1978).Astrophys. J.,221, 937.Google Scholar
  14. 14.
    Chandrasekhar, S. (1970).Phys. Rev. Lett.,24, 611.Google Scholar
  15. 15.
    Friedman, J. L., and Schutz, B. F. (1978).Astrophys. J.,222, 281.Google Scholar
  16. 16.
    Comins, N. (1979).Mon. Not. Roy. Astron. Soc.,189, 233.Google Scholar
  17. 17.
    Comins, N. (1979).Mon. Not. Roy. Astron. Soc.,189, 255.Google Scholar
  18. 18.
    Chandrasekhar, S. (1965).Astrophys. J.,142, 1519.Google Scholar

Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • Kostas D. Kokkotas
    • 1
  • Bernard F. Schutz
    • 1
  1. 1.Department of Applied Mathematics and AstronomyUniversity CollegeCardiffUK

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