The Einstein field equations in the presence of a polytropic fluid performing self‐similar motion are reduced to a dynamical system. Qualitative properties of the dynamical system are investigated in the case when the fluid motion is with shock waves.
REFERENCES
1.
P. J. E. Peebles, The Large Scale Structure of the Universe (Princeton U.P., Princeton, NJ, 1980).
2.
3.
4.
5.
6.
Y. Suto, K. Sato, and H. Sato, “Nonlinear evolution of negative density perturbations in a radiation dominated universe,” preprint.
7.
8.
9.
O. I. Bogoyavlenski, Methods of Qualitative Theory of Dynamical Systems in Astrophyics and Gas Dynamics (Nauka, Moscow, 1980) (in Russian) [English translation (Springer, New York, 1985)].
10.
11.
12.
Rigorously speaking we make the reasonable hypothesis that the separatrix Z is non‐self‐intersecting in the point The opposite case seems pathological and unstable with respect to the variations of the parameter
13.
14.
In this case it is not possible to apply the singularity theorems because these are proved by taking into account only Einstein’s equations, but now we have also used the equation of conservation of mass
This content is only available via PDF.
© 1987 American Institute of Physics.
1987
American Institute of Physics
You do not currently have access to this content.
