Abstract
A model for a time-dependent relativistic “gas” sphere is given. Both pressurep and densityρ are positive inside the outer boundary of the sphere, and they both drop to zero at the boundary itself. Their respective gradients are negative. For expanding models the pressure and the density are decreasing, and for contracting models the pressure and the density are increasing. The adiabatic sound speed is thus real, and for the layers close to the surface of the sphere it is found that the adiabatic sound speed is less than the speed of light. For these layers the conditionρ>3p is also fulfilled. However, the area 4πR 2 for a sphere of constantr is not an increasing function of comoving radial coordinater.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Kramer, D., Stephani, H., MacCallum, M. A., and Herlt, E. (1980).Exact Solutions of Einstein 's Field Equations (Deutsche Verlag der Wissenschaften, Berlin, Cambridge University Press).
Buchdahl, H. A. (1964).Astrophys. J.,140, 1512.
Buchdahl, H. A. (1967).Astrophys. J.,147, 310.
Pant, D. N., and Sah, A. (1982).Phys. Rev. D,26, 1254.
Mehra, A. L. (1980).Gen. Rel. Grav.,12, 187.
Cahill, M. E., and Taub, A. H. (1971).Commun. Math. Phys.,21, 1.
Nariai, H. (1967).Prog. Theor. Phys.,38, 92.
Caporaso, G., and Brecher, K. (1979).Phys. Rev. D,20, 1823.
Zel'dovich, Y. B. (1962).Sov. Phys. JETP,14, 1143.
Mansouri, R. (1977).Ann. Inst. Henri Poincaré,XXVII, 175.
Glass, E. N. (1979).J. Math. Phys.,20, 1508.
Collins, C. B., and Wainwright, J. (1983).Phys. Rev. D,27, 1209.
Srivastava, D. C., and Prasad, S. S. (1983).Gen. Rel. Grav.,15, 65.
McVittie, G. C. (1967).Ann. Inst. Henri Poincaré,V, 1.
Knutsen, H., and Stabell, R. (1979).Ann. Inst. Henri Poincaré,XXXI, 339.
Knutsen, H. (1983).Ann. Inst. Henri Poincaré,XXXIX, 101.
Knutsen, H. (1983).Phys. Scripta,28, 129.
Nariai, H. (1968).Prog. Theor. Phys.,40, 1013.
McVittie, G. C., and Stabell, R. (1968).Ann. Inst. Henri Poincaré,IX, 371.
Misner, C. W. (1968).Astrophysics and General Relativity, Proc. of Brandeis University Summer Institute in Theoretical Physics, (Chrétien, M., Deser, S., and Goldstein, J., eds. Vol. 1, 113. Gordon and Breach, New York).
Robson, E. H. (1972).Ann. Inst. Henri Poincaré,XVI, 41.
Hernandez, W. C., and Misner, C. W. (1966).Astrophys. J.,143, 452.
Thompson, I. H., and Whitrow, G. J. (1967).Mon. Not. R. Astron. Soc.,136, 207.
Glass, E. N. (1979).J. Math. Phys.,20, 1508.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Knutsen, H. Nonstatic gas spheres in general relativity. Gen Relat Gravit 16, 777–788 (1984). https://doi.org/10.1007/BF00762915
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00762915