Astrophysics and Space Science

, Volume 57, Issue 1, pp 203–217 | Cite as

The configuration of a thin, rotating self-similar disk in general relativity

  • Paul S. Wesson
  • A. Lermann


Einstein's equations for a rotating pressure-free space-time are reduced to a system of four first-order non-linear ordinary differential equations in one self-similar dimensionless variable. Numerical results are given for the vacuum solution. A compatible thin disk can be specified by a surface density σ and an angular velocity ω. Self-similarity as a statement of the absence of scales implies that σ and ω can be written asσ=αc2/4πGr, ω=βc/r, and demands that α and β be pure numbers.


Differential Equation General Relativity Angular Velocity Ordinary Differential Equation Surface Density 
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  1. Bardeen, J. and Wagoner, R. V.: 1969,Astrophys. J. 158, L65.Google Scholar
  2. Bardeen, J. and Wagoner, R. V.: 1971,Astrophys. J. 167, 359.Google Scholar
  3. Barenblatt, G. E., and Zel'dovich, Y. B.: 1972,Ann. Rev. Fluid. Mech. 4, 285.Google Scholar
  4. Bonner, W. B. and Faulkes, M. C.: 1967,Monthly Notices Roy. Astron. Soc. 137, 239.Google Scholar
  5. Brandt, J. C.: 1960,Astrophys. J. 131, 293–303.Google Scholar
  6. Burbidge, E. M. and Burbidge, G. R.: 1975, in A. Sandage, M. Sandage and J. Kristian (eds),Galaxies and the Universe, Vol. IX:Stars and Stellar Systems, University of Chicago Press, Chicago, p. 85.Google Scholar
  7. Butterworth, E. M.: 1976,Astrophys. J. 204, 561.Google Scholar
  8. Butterworth, E. M. and Ipser, J. R.: 1976,Astrophys. J. 204, 200.Google Scholar
  9. Cahill, M. E. and Taub, A. H.: 1971,Comm. Math. Phys. 21, 1.Google Scholar
  10. Clark, G. L.: 1947,Proc. Camb. Phil. Soc. 43, 164.Google Scholar
  11. Cocke, W. J.: 1966,J. Math. Phys. 7, 1171.Google Scholar
  12. Freeman, K. C.: 1975, in A. Sandage, M. Sandage and J. Kristian (eds),Galaxies and the Universe, Vol. IX:Stars and Stellar Systems, University of Chicago Press, Chicago, p. 466.Google Scholar
  13. Gödel, K.: 1949,Rev. Mod. Phys. 21, 447.Google Scholar
  14. Hartle, J. B. and Sharp, D. H.: 1967,Astrophys. J. 147, 317.Google Scholar
  15. Heckmann, O.: 1961,Astron. J. 66, 599.Google Scholar
  16. Heckmann, O. and Schücking, E.: 1962, in L. Witten (ed.),Gravitation — An Introduction to Current Research, Wiley, New York, p. 438.Google Scholar
  17. Henriksen, R. N. and Wesson, P. S.: 1978,Astrophys. Space Sci. 53, 429.Google Scholar
  18. Hunter, C.: 1963,Monthly Notices Roy. Astron. Soc. 126, 299.Google Scholar
  19. Israel, W.: 1966,Il Nuovo Cimento 44B, 1.Google Scholar
  20. Israel, W.: 1967a,Il Nuovo Cimento 48B, 463.Google Scholar
  21. Israel, W.: 1967b,Phys. Rev. 153, 1388.Google Scholar
  22. Kerr, R. P.: 1963,Phys. Rev. Letters 11, 237.Google Scholar
  23. King, A. R.: 1974,Comm. Math. Phys. 38, 157.Google Scholar
  24. Kohler, V. M.: 1933,Ann. Phys. 16, 129.Google Scholar
  25. Marder, L.: 1958a,Proc. Roy. Soc. London A244, 524.Google Scholar
  26. Marder, L.: 1958b,Proc. Roy. Soc. London A246, 133.Google Scholar
  27. Marder, L.: 1959,Proc. Roy. Soc. London A252, 45.Google Scholar
  28. Mavrides, S.: 1976,Monthly Notices Roy. Astron. Soc. 177, 709.Google Scholar
  29. Mestel, L.: 1963,Monthly Notices Roy. Astron. Soc. 126, 553.Google Scholar
  30. Misner, C. W., Thorne, K. S. and Wheeler, J. A.: 1973,Gravitation, Freeman, San Francisco, p. 551.Google Scholar
  31. Morgan, T. and Morgan, L.: 1969,Phys. Rev. 183, 1097.Google Scholar
  32. Papapetrou, A.: 1976a,Ann. Inst. Henri Poincaré 24A, 165.Google Scholar
  33. Papapetrou, A.: 1976b,Ann. Inst. Henri Poincaré 24A, 171.Google Scholar
  34. Raychaudhuri, A.: 1958,Proc. Phys. Soc. London 72, 263.Google Scholar
  35. Raychaudhuri, A. and Som, M. M.: 1962,Proc. Camb. Phil. Soc. 58, 338.Google Scholar
  36. Salpeter, E. E. and Wagoner, R. V.: 1971,Astrophys. J. 164, 557.Google Scholar
  37. Sneddon, I.: 1966,Mixed Boundary Problems in Potential Theory, North Holland, Amsterdam.Google Scholar
  38. Synge, J. L.: 1966,Relativity: The General Theory, North Holland, Amsterdam.Google Scholar
  39. Teixera, A. F. da F. and Som. M. M.: 1974,Il Nuovo Cimento 21B, 64Google Scholar
  40. Toomre, A.: 1963,Astrophys. J. 138, 385.Google Scholar
  41. Toomre, A.: 1964,Astrophys. J. 139, 1217.Google Scholar
  42. van Stockum, W. J.: 1936,Proc. Roy. Soc. Edinburgh 57, 135.Google Scholar
  43. Wagoner, R. V.: 1965,Phys. Rev. 138, B1583.Google Scholar
  44. Wesson, P. S.: 1978,Cosmology and Geophysics, Hilger, Bristol (in press).Google Scholar
  45. Weyl, H.: 1917,Ann. Rev. Phys. 54, 117.Google Scholar
  46. Wright, J. P.: 1965,J. Math. Phys. 6, 103.Google Scholar
  47. Wyse, A. B. and Mayall, N. U.: 1942,Astrophys. J. 95, 24.Google Scholar

Copyright information

© D. Reidel Publishing Company 1978

Authors and Affiliations

  • Paul S. Wesson
    • 1
  • A. Lermann
    • 2
  1. 1.St John's CollegeCambridge UniversityEngland
  2. 2.Oslo UniversityNorway

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