论文标题
Schwarzschild Black String外部的Gregory-Laflamme不稳定
The Gregory-Laflamme Instability of the Schwarzschild Black String Exterior
论文作者
论文摘要
在本文中，提出了五维Schwarzschild Black String的Gregory-Laflamme不稳定性的直接严格数学证明。在选择Ansatz的扰动和量规选择的情况下，线性化真空爱因斯坦方程将单个函数的ode问题减少到ode问题。在这项工作中，应用了变量的合适重新缩放和更改，将颂歌铸成分配了能量功能的schrödinger特征值方程。然后通过直接的变分方法显示，最低的本征功能会产生指数增长的模式解决方案，该解决方案在未来的事件范围内具有可允许的行为，并呈空格般的无穷大。添加纯量规溶液后，这引起了谐波/横向无跟踪仪表中线性化真空级的正常生长模式溶液。
In this paper, a direct rigorous mathematical proof of the Gregory-Laflamme instability for the five-dimensional Schwarzschild black string is presented. Under a choice of ansatz for the perturbation and a gauge choice, the linearised vacuum Einstein equation reduces to an ODE problem for a single function. In this work, a suitable rescaling and change of variables is applied which casts the ODE into a Schrödinger eigenvalue equation to which an energy functional is assigned. It is then shown by direct variational methods that the lowest eigenfunction gives rise to an exponentially growing mode solution which has admissible behavior at the future event horizon and spacelike infinity. After the addition of a pure gauge solution, this gives rise to a regular exponentially growing mode solution of the linearised vacuum Einstein equation in harmonic/transverse-traceless gauge.
