线性扰动D型时空的Petrov型
Petrov type of linearly perturbed type D spacetimes
摘要：
我们证明了满足线性化真空爱因斯坦方程的D型背景下的时空一般是I型时空，并且主方向分裂和Weyl张量简并本征值分裂是度规微扰参数的非解析函数.这提供了一个规范不变的表征的影响的扰动的基础几何，而不呼吁微分曲率不变量。这是特别感兴趣的史瓦西解决方案，其中有没有签名的代数曲率不变量上的均匀扰动。我们还表明，与一般情况下，不稳定的什至模式的史瓦西裸奇点变形的外尔张量到II型之一。
英文摘要：
We show that a spacetime satisfying the linearized vacuum Einstein equations around a type D background is generically of type I, and that the splittings of the Principal Null Directions (PNDs) and of the degenerate eigenvalue of the Weyl tensor are non analytic functions of the perturbation parameter of the metric. This provides a gauge invariant characterization of the effect of the perturbation on the underlying geometry, without appealing to differential curvature invariants. This is of particular interest for the Schwarzschild solution, for which there are no signatures of the even perturbations on the algebraic curvature invariants. We also show that, unlike the general case, the unstable even modes of the Schwarzschild naked singularity deforms the Weyl tensor into a type II one.
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