TAILIEUCHUNG - Đề tài " Stability and instability of the Cauchy horizon for the spherically symmetric Einstein-Maxwell-scalar field equations "

This paper considers a trapped characteristic initial value problem for the spherically symmetric Einstein-Maxwell-scalar field equations. For an open set of initial data whose closure contains in particular Reissner-Nordstr¨m data, o the future boundary of the maximal domain of development is found to be a light-like surface along which the curvature blows up, and yet the metric can be continuously extended beyond it. This result is related to the strong cosmic censorship conjecture of Roger Penrose. . | Annals of Mathematics Stability and instability of the Cauchy horizon for the spherically symmetric Einstein-Maxwell-scalar field equations By Mihalis Dafermos Annals of Mathematics 158 2003 875 928 Stability and instability of the Cauchy horizon for the spherically symmetric Einstein-Maxwell-scalar field equations By Mihalis Dafermos Abstract This paper considers a trapped characteristic initial value problem for the spherically symmetric Einstein-Maxwell-scalar field equations. For an open set of initial data whose closure contains in particular Reissner-Nordstrom data the future boundary of the maximal domain of development is found to be a light-like surface along which the curvature blows up and yet the metric can be continuously extended beyond it. This result is related to the strong cosmic censorship conjecture of Roger Penrose. 1. Introduction The principle of determinism in classical physics is expressed mathematically by the uniqueness of solutions to the initial value problem for certain equations of evolution. Indeed in the context of the Einstein equations of general relativity where the unknown is the very structure of space and time uniqueness is equivalent on a fundamental level to the validity of this principle. The question of uniqueness may thus be termed the issue of the predictability of the equation. The present paper explores the issue of predictability in general relativity. Since the work of Leray it has been known that for the Einstein equations contrary to common experience uniqueness for the Cauchy problem in the large does not generally hold even within the class of smooth solutions. In other words uniqueness may fail without any loss in regularity such failure is thus a global phenomenon. The central question is whether this violation of predictability may occur in solutions representing actual physical processes. Physical phenomena and concepts related to the general theory of relativity namely gravitational collapse black holes .

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