Abstract
The boundary conditions for the gravitational and electromagnetic fields on charged shells are formulated. The shells are characterized in geometrical terms and the boundary conditions are manifestly covariant. The formalism is applied to the study of the gravitational collapse of homogeneous charged spherical shells. The law of conservation of energy, obtained by integrating the equations of motion of the shell and interpreted in full analogy with the special theory of relativity, is the starting point in analyzing the equilibrium states and the motion of the shells. It is concluded that no charge, however high it may be, can stop the gravitational collapse of the shell below the upper Nordström radius.
Similar content being viewed by others
References
Harrison B. K., Thorne K. S., Wakano M., Wheeler J. A.: Gravitational Theory and Gravitational Collapse. Chicago and London 1965.
Oppenheimer J. R., Snyder, H.: Phys. Rev.56 (1939), 455.
Bonnor W. B.: Nature204 (1964), 868.
Bonnor W. B.: Z. f. Physik160 (1960), 59.
Bonnor W. B.: Monthly Not. Roy. Astr. Soc.129 (1965), 443.
Lanczos K.: Physik. Z.23 (1922), 539.
Lanczos K.: Ann. d. Physik74 (1924), 518.
O'Brien St., Synge J. L.: Commun. Dublin Inst. Adv. Stud. A No.9 (1952).
Lichnerowicz A.: Théories relativistes de la gravitation et de l'électromagnétisme. Paris 1955.
Taub A. H.: Ill. J. Math.1 (1957), 370.
Dautcourt G.: Math. Nachr.27 (1964), 277.
Israel W.: Il Nuovo Cim.X 44 (1966), 1.
Israel W.: Il Nuovo Cim.X 48 (1967), 463.
Israel W.: Phys. Rev.153 (1967), 1388.
Florides P. S.: Proc. Camb. Phil. Soc.58 (1962), 110.
Arnowitt R., Deser S., Misner C. W.: Phys. Rev.120 (1960), 321. There are references to other articles on the same problem.
Bruhat Y.:in Gravitation: an Introduction to Current Research. New York and London 1963.
Synge J. L.: The Relativistic Gas. Amsterdam 1957.
Møller C.: The Theory of Relativity. Oxford 1952.
Zel'dovich Ya. B., Novikov J. D.:in Einsteinovskij sbornik. Moskva 1966.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kuchař, K. Charged shells in general relativity and their gravitational collapse. Czech J Phys 18, 435–463 (1968). https://doi.org/10.1007/BF01698208
Issue Date:
DOI: https://doi.org/10.1007/BF01698208