Abstract It is shown that negative Einstein metrics are attractors of the Einstein-Klein-Gordon system. As an essential part of the proof we upgrade a technique that uses the continuity equation complementary to L2-estimates to control massive matter fields. In contrast to earlier applications of this idea we require a correction to the energy density to obtain sufficiently strong pointwise bounds.

中文翻译：

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爱因斯坦-克莱因-戈登系统的吸引子

摘要 证明负爱因斯坦度量是爱因斯坦-克莱因-戈登系统的吸引子。作为证明的重要部分，我们升级了一种技术，该技术使用与 L2 估计互补的连续性方程来控制大量物质场。与这个想法的早期应用相反，我们需要对能量密度进行修正以获得足够强的逐点边界。