Analysis on superradiant instability of charged dilaton Black Hole

Abstract

In this post, a new variable y($\mu =y\omega$) is added to extend the results of the above post. We derive a very compact resonance formulation. When y is a certain limit, the effective potential of the equation exists at the pole, and the potential well appears outside the event horizon, when $e^{-4\alpha \Phi /(n-1)}\sqrt{\alpha }Q\ll r_{+}\ll 1/(\frac{4}{n-1}y)$, so charged dilator black hole is superradiatively unstable at this time.