Analysis on superradiant instability of charged dilaton Black Hole

TL;DR

This paper investigates the superradiant instability of charged dilaton black holes by introducing a new variable and deriving a compact resonance formulation, identifying conditions under which the black hole becomes unstable.

Contribution

It extends previous analyses by adding a new variable and deriving a resonance formulation to better understand superradiant instability conditions.

Findings

Superradiant instability occurs when certain potential conditions are met.

A new variable y helps analyze the resonance behavior.

Conditions for instability depend on charge, dilaton coupling, and horizon radius.

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.