论文标题
缓慢旋转的Kerr-De保姆家族的线性稳定性
Linear stability of the slowly-rotating Kerr-de Sitter family
论文作者
论文摘要
在本文中，我们证明了黑洞的缓慢旋转的Kerr-de保姆家族是线性稳定的，这是对Einstein真空方程的一种解决方案，具有$λ> 0 $ 0 $的谐波（Wave）。本文是系列的一部分，该系列提供了一个新颖的证据，证明了缓慢旋转的Kerr-De保姆家族的全面稳定性。本文及其后续措施通过将准模式将准模式解释为hilbert空间上操作员的$ h^k $特征值，从而提供了Kerr-de保姆家族的非线性稳定性，从而从Hintz和Vasy的原始作品中提供了一种替代方法。特别是，我们避免构建分解的依然形态延续。我们也不压缩时空，因此避免使用$ b $ - 钙库，而仅在被困组的附近使用标准的伪差异参数；并避免完全阻尼。当前论文中的方法提供了一个明确的示例，介绍了如何使用vectorfield方法在诱捕背景上实现分解估计。
In this paper, we prove that the slowly-rotating Kerr-de Sitter family of black holes are linearly stable as a family of solutions to the Einstein vacuum equations with $Λ>0$ in harmonic (wave) gauge. This article is part of a series that provides a novel proof of the full nonlinear stability of the slowly-rotating Kerr-de Sitter family. This paper and its follow-up offer a self-contained alternative approach to nonlinear stability of the Kerr-de Sitter family from the original work of Hintz and Vasy by interpreting quasinormal modes as $H^k$ eigenvalues of an operator on a Hilbert space, and using integrated local energy decay estimates to prove the existence of a spectral gap. In particular, we avoid the construction of a meromorphic continuation of the resolvent. We also do not compactify the spacetime, thus avoiding the use of $b$-calculus and instead only use standard pseudo-differential arguments in a neighborhood of the trapped set; and avoid constraint damping altogether. The methods in the current paper offer an explicit example of how to use the vectorfield method to achieve resolvent estimates on a trapping background.
