论文标题
黑洞和裸奇异的线性稳定性
Linear Stability of Black Holes and Naked Singularities
论文作者
论文摘要
这些笔记来自于2021年9月30日至10月5日在巴西瓜拉帕里（Esp \'ıritosanto）在巴西瓜拉帕里（Esp \'ıritosanto）举行的VJosépl\'ınioBaptista宇宙学学校提供的课程。简要引入并用来证明Kerr-Newman家族以及Cauchy Horizons以外的内部黑洞区域是不稳定的，因此是不稳定的，因此是不稳定的，因此，标准的模态方法是利用背景对称性并分别分析线性扰动的谐波组成部分的分别分析。证明需要对及时边界处的边界条件进行处理，这是详细给出的。然后引入非模式线性稳定性概念，并用来证明具有非负宇宙常数的Schwarzschild黑洞的外部通信域满足了这种更强大的稳定性条件，从而排除了扰动的瞬态增长，并且还表明，黑洞有效地将黑洞沉降到缓慢旋转的Kerr黑色旋转黑洞。讨论了仪表不变曲率标量中的扰动场的编码以及扰动对时空几何形状的影响。
These notes follow from a course delivered at the V José Pl\'ınio Baptista School of Cosmology, held at Guarapari (Esp\'ırito Santo) Brazil, from 30 September to 5 October 2021. A review of the current status of the linear stability of black holes and naked singularities is given. The standard modal approach, that takes advantage of the background symmetries and analyze separately the harmonic components of linear perturbations, is briefly introduced and used to prove that the naked singularities in the Kerr--Newman family, as well as the inner black hole regions beyond Cauchy horizons, are unstable and therefore unphysical. The proofs require a treatment of the boundary condition at the timelike boundary, which is given in detail. The nonmodal linear stability concept is then introduced, and used to prove that the domain of outer communications of a Schwarzschild black hole with a non-negative cosmological constant satisfies this stronger stability condition, which rules out transient growths of perturbations, and also to show that the perturbed black hole settles into a slowly rotating Kerr black hole. The encoding of the perturbation fields in gauge invariant curvature scalars and the effects of the perturbation on the geometry of the spacetime is discussed.
