Abstract
In their classic 1939 paper Oppenheimer and Snyder introduced the first mathematical model for gravitational collapse of stars based on spherically symmetric solutions of the Einstein gravitational field equations. In this exact solution of the Einstein equations, the boundary surface of a massive fluid sphere falls continuously into a black hole and the dynamics is described by exact formulas. This provided the first solid evidence for the idea that black holes could form from gravitational collapse in massive stars. The Oppenheimer—Snyder paper also provided the first example in which a solution of the Einstein equations having interesting dynamics was constructed by using the covariance of the equations to match two simpler solutions across an interface. The Oppenheimer—Snyder model requires the simplifying assumption that the pressure be identically zero. In this article we construct shock wave generalizations of the Oppenheimer—Snyder model that apply to the case when the pressure is nonzero. A general characterization of shock wave interfaces in solutions of the Einstein equations is presented in Section 2, and examples are derived and discussed in detail in the later sections.
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Smoller, J., Temple, B. (2001). Shock Wave Solutions of the Einstein Equations: A General Theory with Examples. In: Freistühler, H., Szepessy, A. (eds) Advances in the Theory of Shock Waves. Progress in Nonlinear Differential Equations and Their Applications, vol 47. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0193-9_3
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DOI: https://doi.org/10.1007/978-1-4612-0193-9_3
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