论文标题
Schwarzschild上分离的Lichnerowicz张量波方程的显式三角脱钩到标量regge-wheeler方程
Explicit Triangular Decoupling of the Separated Lichnerowicz Tensor Wave Equation on Schwarzschild into Scalar Regge-Wheeler Equations
论文作者
论文摘要
我们考虑了Schwarzschild时空上的向量和Lichnerowicz波方程，这对应于谐波仪（或在Lorenz和de Donder gauges中）中的麦克斯韦和线性化的爱因斯坦方程。在变量完全分离后，径向模式方程形成了耦合线性ODE的复杂系统。我们概述了将这些系统切换为稀疏三角形形式的精确抽象策略，其中对角线块由旋转$ s $ suble starar regge-wheeler方程组成（用于旋转$ s = 0,1,1,2 $）。我们以前已经处理过的矢量波方程的示例，我们成功地完成了利希纳罗维奇波方程策略的实施。我们的结果比以前在文献中进行了更多的临时尝试，提出了完整而最大的最终三角形形式。这些结果在谐波仪表中的schwarzschild黑洞的电磁和重力扰动的量子场理论以及经典稳定性分析中具有重要应用。
We consider the vector and the Lichnerowicz wave equations on the Schwarzschild spacetime, which correspond to the Maxwell and linearized Einstein equations in harmonic gauges (or, respectively, in Lorenz and de Donder gauges). After a complete separation of variables, the radial mode equations form complicated systems of coupled linear ODEs. We outline a precise abstract strategy to decouple these systems into sparse triangular form, where the diagonal blocks consist of spin-$s$ scalar Regge-Wheeler equations (for spins $s=0,1,2$). Building on the example of the vector wave equation, which we have treated previously, we complete a successful implementation of our strategy for the Lichnerowicz wave equation. Our results go a step further than previous more ad-hoc attempts in the literature by presenting a full and maximally simplified final triangular form. These results have important applications to the quantum field theory of and the classical stability analysis of electromagnetic and gravitational perturbations of the Schwarzschild black hole in harmonic gauges.
