Instability of charged Lovelock black holes: Vector perturbations and scalar perturbations

We examine the stability of charged Lovelock black hole solutions under vector-type and scalar-type perturbations. We find suitable master variables for the stability analysis; the equations for these variables are Schrodinger-type equations with two components, and these Schrodinger operators are symmetric. By these master equations, we show that charged Lovelock black holes are stable under vector-type perturbations. For scalar-type perturbations, we show the criteria for instability and check these numerically. In our previous paper [T. Takahashi, Prog. Theor. Phys. 125, 1289 (2011)], we have shown that nearly extreme black holes show instability under tensor-type perturbations. In this paper, we find that black holes with a small charge show instability under scalar-type perturbations even if they have a relatively large mass.