Gauge Invariant Perturbations of General Spherically Symmetric Spacetimes

In this paper, the gauge choices in general spherically symmetric spacetimes have been explored. We construct the gauge invariant variables and the master equations for both the Detweiler easy gauge and the Regge-Wheeler gauge, respectively. The particular cases for $l=0,1$ are also been investigated. Our results provide analytical calculations of metric perturbation in general spherically symmetric spacetimes, which can be applied to various cases, including the Effective-One-Body problem. A simple example is presented to show how the metric perturbation components are related to the source perturbation terms.