论文标题
在球形对称性下，爱因斯坦 - 标准场系统的多项式爆破上限
Polynomial Blow-up Upper Bounds for the Einstein-scalar field System Under Spherical Symmetry
论文作者
论文摘要
对于一般重力崩溃，在黑洞区域内，可能会出现奇异性$（r = 0）$。在本文中，我们旨在回答这些奇点的强大。我们分析各种几何量的行为。特别是，我们表明，在最单一的情况下，Kretschmann标量遵守多项式上限上限$ O（1/r^n）$。这改善了以前最著名的双指数上限$ o \ big（\ exp \ exp（1/r）\ big）$。我们的结果是敏锐的，因为有一些已知的例子表明，没有亚物质上限可以保持。最后，我们对Schwarzschild解决方案的扰动进行了案例研究。
For general gravitational collapse, inside the black-hole region, singularities $(r=0)$ may arise. In this article, we aim to answer how strong these singularities could be. We analyse the behaviours of various geometric quantities. In particular, we show that in the most singular scenario, the Kretschmann scalar obeys polynomial blow-up upper bounds $O(1/r^N)$. This improves previously best-known double-exponential upper bounds $O\big(\exp\exp(1/r)\big)$. Our result is sharp in the sense that there are known examples showing that no sub-polynomial upper bound could hold. Finally we do a case study on perturbations of the Schwarzschild solution.
