On the Non-Linear Behavior of Nonspherical Perturbations in Relativistic Gravitational Collapse

概要

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As a preparation for clarifying the final state of relativistic gravitational collapse, we examine how nonspherical perturbations behave in the neighbourhood of the Schwarzschild surface, by analyzing the second-order non-linear perturbations as well as the first-order linear ones, and we find that through the self-interaction of the perturbations corresponding to incoming gravitational waves reflected by the potential barrier, the non-linear effect becomes important, when the waves approach the Schwarzschild surface together with the surface of the collapsing object. Consequently, the conclusion derived in the linear approximation is questionable that the final gravitational state is expressed by the Schwarzschild or Kerr field. It is concluded that, however small the initial nonspherical perturbations are, full non-linearity must be considered, in order to analyze dynamical processes in the neighbourhood of the final state.
理論物理学刊行会の論文
1974-10-25