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Description

Given that shock-waves are astrophysical, and that the general theory of relativity contains phenomena not present in Newtonian gravitational theory, an attempt to apply the mathematical theory of shock-waves to fluids whose motion is governed by Einstein's equations is natural. There is no {it a priori} reason these methods should succeed given the dynamical interactions between matter and spacetime, the possible formation of black holes and curvature singularities, and of equal seriousness, coordinate singularities.

Recent work by Jeff Groah and Blake Temple show the consistency of the mathematical theory of shock-waves and the general theory of relativity for spherically symmetric solutions of the Einstein equations for a perfect fluid. We further show that in spacetimes with small total mass concentrated outside a spherical star and with some restriction on the total variation of the data, black holes do not form, and existence of shock-wave solutions can be guaranteed for all time.