Abstract
We examine the stability of charged Lovelock black hole solutions under vector type and scalar type perturbations. We find the suitable master variables for the stability analysis; the equations for these variables are the 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 the instability and check these numerically. In our previous paper, we have shown that nearly extremal black holes have the instability under tensor type perturbations. In this paper, we find that black holes with small charge have the instability under scalar type perturbations even if they have relatively large mass.
Highlights
The braneworld scenario with large extra dimensions predicts that higher dimensional black holes might be produced at colliders [1]
We have studied the stability of charged Lovelock black hole solutions
We have shown that the Schrodinger operator for this type perturbations is an essentially positive definite self adjoint operator
Summary
The braneworld scenario with large extra dimensions predicts that higher dimensional black holes might be produced at colliders [1]. These are Shrodinger type equations and they have shown that these Shrodinger operators are all positive definite using the S-deformation approach which they have developed by Friedrichs extension These results show that Schwarzschild black holes are stable in higher dimensions. For this Lovelock black hole solution, the stability has been analyzed in [17,18,19] In these papers, it has been shown that black holes with sufficiently small mass are unstable under scalar type perturbations in odd dimensions and unstable under tensor type perturbations in even dimensions. In this paper, we’d like to extend the stability analysis for Lovelock black hole solutions to charged Lovelock black hole solutions For this charged solution, stability analysis under tensor type perturbations has been examined by us and we have shown that black holes are unstable if they have nearly extremal mass [20].
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