论文标题
稳定的空间样奇异性形成，用于公理对称和偏光近距离雪Warzschild Black Hole Interiors
Stable space-like singularity formation for axi-symmetric and polarized near-Schwarzschild black hole interiors
论文作者
论文摘要
我们显示了爱因斯坦真空方程的Schwarzschild奇异性（黑洞区域内）的稳定性结果。结果在极化轴向对称性的类别中得到了证明，在shwarzschild数据的扰动下，在超出表面$ \ {r = \ e \} $上，$ \ e << 2m $。我们的结果只是部分稳定性结果，因为我们表明，尽管（类似太空的）奇异性仍然存在于上述扰动下，但接近奇异性的度量的行为比Schwarzschild解决方案更重要。实际上，我们发现该解决方案显示出渐近性的学期动力学，并在奇异性的每个点接近不同的Kasner解决方案。这些Kasner型渐近学远离各向异性，因为（如在Schwarzschild中）有两个合同方向，一个方向有两个。 我们的证明取决于能量方法和轴向对称性的新方法，我们认为这具有更大的适用性：在这种对称性类别和在合适的地球仪表下，可以将夏娃作为自由波和（非线性）频率耦合，这对预计的几何形状进行了2+1+1+1+1+1+1+1+1+。 ODES描述了爱因斯坦方程的非线性部分的事实，是人们如何克服奇异性表现出的某种线性不稳定性的核心。
We show a stability result for the Schwarzschild singularity (inside the black hole region) for the Einstein vacuum equations. The result is proven in the class of polarized axial symmetry, under perturbations of the Schwarzschild data induced on a hypersurface $\{r=\e\}$, $\e<<2M$. Our result is only partly a stability result, in that we show that while a (space-like) singularity persists under perturbations as above, the behaviour of the metric approaching the singularity is much more involved than for the Schwarzschild solution. Indeed, we find that the solution displays asymptocially-velocity-term-dominated dynamics and approaches a different Kasner solution at each point of the singularity. These Kasner-type asymptotics are very far from isotropic, since (as in Schwarzschild) there are two contracting directions and one expanding one. Our proof relies on energy methods and on a new approach to the EVE in axial symmetry, which we believe has wider applicability: In this symmetry class and under a suitable geodesic gauge, the EVE can be studied as a free wave coupled to (nonlinear) ODEs, which couple the geometry of the projected, 2+1 space-time to the free wave. The fact that the nonlinear part of the Einstein equations is described by ODEs lies at the heart of how one can overcome a certain linear instability exhibited by the singularity.
