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Shock waves and general relativity. (English) Zbl 0870.53063
In 1939, J. R. Oppenheimer and H. Snyder produced the first mathematical model for the gravitational collapse of stars [Phys. Rev. 56, 455-459 (1939)]. This involved the matching of two metrics (the Robertson-Walker metric and the Schwarzschild metric), Lipschitz continuously across a surface of discontinuity for the fluid variables. In their paper, they also deduced the theoretical existence of what we now call black holes. However, they had to make the (unphysical) assumption that the pressure was always equal to zero. In this paper, we shall describe how their results can be extended to the case of nonzero pressure. In order to do this, we shall first clarify the role of “conservation” in stellar and cosmological models, and then we shall study shock waves in general relativity. Finally we shall describe a possible physical application of our result to dynamic models of cosmology.
[See also the following review Zbl 0870.53064].

53Z05 Applications of differential geometry to physics
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
83C40 Gravitational energy and conservation laws; groups of motions
76L05 Shock waves and blast waves in fluid mechanics
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
Zbl 0870.53064
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