Schwarzschild-Tangherlini quasinormal modes at large $D$ revisited

The large dimension ($D$) limit of general relativity has been used in problems involving black holes as an analytical approximation tool. Further it has been proposed that both linear and nonlinear problems involving black holes can be systematically studied in a $1/D$ expansion. Certain quasinormal modes of higher-dimensional Schwarzschild black holes with $\omega \sim \mathcal{O}(1)$ were studied in the large $D$ limit using a $1/D$ expansion for the mode function. In this paper, we revisit this linear perturbation problem and obtain an analytical equation for the vector quasinormal modes $\omega \sim \mathcal{O}(1)$ in the large $D$ limit, without using a $1/D$ expansion for the mode function. This can be used to compute quasinormal modes to next to leading order in $1/D$. We also compute vector and scalar quasinormal modes with $\omega \sim \mathcal{O}(D)$ in the Laplace transform approach in the large $D$ limit. We discuss the useful features of this approach specifically in the large $D$ limit.