标题： 红十字国际委员会2023年会议录：施瓦西背景时空上$l=0,1$模式扰动的规范不变处理提案 显示英文标题

标题： ICRC2023 Proceedings: Proposal of a gauge-invariant treatment of $l=0,1$-mode perturbations on the Schwarzschild background spacetime

摘要： 从2003年起，人们开始发展在一般背景时空上的规范不变微扰理论，“零模问题”被提出作为该理论中的本质问题。 在施瓦西背景时空上的微扰理论中，$l=0,1$模式对应于上述“零模”，而这些模式的规范不变处理是施瓦西背景时空上微扰理论中的著名非平凡问题。 由于这种状况，提出了这些$l=0,1$-模微扰的规范不变处理方法。 通过这种规范不变处理方法，得到了这些模式在一般物质场下的线性化爱因斯坦方程的解。 在真空情况下，确认了克尔时空唯一性定理的线性化版本以规范不变的方式成立。 从这个意义上说，我们的提议是合理的。 显示英文摘要

摘要： A gauge-invariant perturbation theory on a generic background spacetime is developing from 2003 and ``zero-mode problem'' for linear metric perturbations was proposed as the essential problem of this theory. In the perturbation theory on the Schwarzschild background spacetime, $l=0,1$ modes correspond to the above ``zero-mode'' and the gauge-invariant treatments of these modes is a famous non-trivial problem in perturbation theories on the Schwarzschild background spacetime. Due to this situation, a gauge-invariant treatment for these $l=0,1$-mode perturbations is proposed. Through this gauge-invariant treatment, the solutions to the linearized Einstein equation for these modes with a generic matter field are derived. In the vacuum case, the linearized version of uniqueness theorem of Kerr spacetime is confirmed in a gauge-invariant manner. In this sense, our proposal is reasonable.