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The Initial Value Problem for Self-Gravitating Fluid Bodies

In: Mathematical Physics X

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  • Alan D. Rendall

    (Max-Planck-Institut für Astrophysik)

Abstract

Surprisingly little is known concerning the initial value problem for material bodies within the Newtonian and Einsteinian theories of gravity. An understanding of this question has an obvious significance for the study of the problem of motion in these two theories. The following is a summary of some new results concerning the case where the matter model chosen is a perfect fluid. The fact that fluid bodies are being described will be encoded by the assumption that the matter density has spatially compact support; it is important to note that replacing this by the requirement that the density tends to zero at infinity at each fixed time does not lead to a significant simplification. In this section results concerning local in time existence will be discussed while in the following section some global statements will be collected.

Suggested Citation

  • Alan D. Rendall, 1992. "The Initial Value Problem for Self-Gravitating Fluid Bodies," Springer Books, in: Konrad Schmüdgen (ed.), Mathematical Physics X, pages 470-474, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-77303-7_54
    DOI: 10.1007/978-3-642-77303-7_54
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