Eigenvalue spectrum of marginally outer trapped surface stability operator in the Weyl-distorted Schwarzschild black holes

Marginally outer trapped surfaces (MOTS) are closed spacelike surfaces from which outgoing light rays neither converge nor diverge. In recent years they have been found to be a key tool for understanding black hole geometries. In particular, the stability operator provides information on whether the marginally outer trapped surfaces (MOTS) bounds a trapped region. This study investigates the eigenvalue problem associated with the stability operator for MOTS in the context of Weyl-distorted Schwarzschild solutions. By solving the eigenvalue problem, we aim to understand whether these solutions can always be understood as black holes.