Abstract
We construct the energy-momentum tensor in Minkowskian space-time for Einstein's collisionless system of test particles moving in concentric circles and obtain the four-force necessary to preserve equilibrium. We derive a tensor field, satisfying the linearized Einstein equations, which is consistent with the applied four-force. If the particles are contained within a sphere, then outside the sphere we show that the tensor field is a linearized Schwarzschild fieldwith a cosmological constant (this constant being the “potential energy” calculated on the surface of the sphere).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Einstein, A. (1939).Ann Math.,40, 922.
Gilbert, C. (1954).Mon. Not. R. Astr. Soc.,114, 628.
Harrison, B. K., Thorne, K. S., Wakano, M., and Wheeler, J. A. (1965).Gravitational Theory and Gravitational Collapse (University of Chicago Press, Chicago), p. 54.
Datta, B. K. (1970).Gen. Rel. Grav.,1, 19.
Bondi, H. (1971).Gen. Rel. Grav.,2, 321.
Hogan, P. A. (1973).Proc. R. Ir. Acad.,73A, 91.
Israel, W. (1966).Nuovo Cimento,44B, 1.
Evans, A. B. (1977).Gen. Rel. Grav.,8, 155.
Synge, J. L. (1966).Relativity: The General Theory (North-Holland Publishing Company, Amsterdam), p. 109.
Synge, J. L. (1967).Proc. R. Ir. Acad.,65A, 27.
Hawking, S. W., and Ellis, G. F. R. (1973).The Large-Scale Structure of Space-Time (Cambridge University Press, Cambridge), p. 89.
Synge, J. L. (1965).Relativity: The Special Theory (North-Holland Publishing Company, Amsterdam), p. 299.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hogan, P.A. A reconstruction in Minkowskian space-time of Einstein's assembly of test particles. Gen Relat Gravit 9, 1021–1030 (1978). https://doi.org/10.1007/BF00784662
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00784662