Exact solutions of the spherically symmetric gravitational field equations

Abstract

The Einstein gravitational equations in the spherically symmetric case and for the dust model (i.e., p = 0) have been studied by several authors. However, the solutions obtained by them are not completed yet, and the corresponding metric is written in implicit forms which is inconvenient for physical problems. In the present paper we make the following improvements: (1) We obtain all spherical solutions for the dust model with explicit expressions which consist of three classes and an exceptional case; (2) All these solutions contain singularities which are analyzed together with their physical properties.

Keywords

gravitational equations / spherically symmetry / 41A05 / 41A25 / 30D10 / 30D15

References

[1] Oppenheimer J. R., Snyder H. Phys. Rev., 1939, 56: 455

[2] May M. M., White T. H. Phys. Rev., 1966, 141: 1232

[3] Landau L. D. and Lifscitz E. M., Field Theory (Chinese Translation), 1959, 345

[4] Bondi H., Mon. Not. R. Astr. Soc., 1947, 107, 410

[5] Han J., Journal of Nanjing University, 1965

[6] Bonnor W. B., Mon. Not. R. Astr. Soc., 1972, 159, 261

[7] Gu C., Journal of Fudan University (Natural Science), 1973, 3

[8] Hu H. S. (HU He-sheng), Abstracts of Contributed Papers, Ninth International Conference on General Relativity and Gravitation (GR9), Jena, East Germany, July 14–19, 1980